Method and apparatus for video coding

ABSTRACT

A method of video decoding for a decoder is provided. In the method, prediction information of a current block in a current picture is decoded from a coded video bitstream, where the prediction information is indicative of an inter prediction mode. Whether a filtering process is applied on the current block is determined, where the filtering process adjusts inter prediction samples of the current block based on neighboring reconstructed samples of the current block. A primary transform is thus performed for a transform block according to a pre-defined primary transform type based on that the filtering process is determined to be applied on the current block, where the transform block is partitioned from the current block.

INCORPORATION BY REFERENCE

This present application claims the benefit of priority to U.S.Provisional Application No. 62/857,141, “IMPLICIT TRANSFORM FOR INTERPREDICTION MODES” filed on Jun. 4, 2019, and U.S. ProvisionalApplication No. 62/892,238, “HIGH-LEVEL SYNTAX ON PRIMARY TRANSFORM”filed on Aug. 27, 2019. The entire disclosures of the prior applicationsare hereby incorporated by reference in their entirety.

TECHNICAL FIELD

The present disclosure describes embodiments generally related to videocoding.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Video coding and decoding can be performed using inter-pictureprediction with motion compensation. Uncompressed digital video caninclude a series of pictures, each picture having a spatial dimensionof, for example, 1920×1080 luminance samples and associated chrominancesamples. The series of pictures can have a fixed or variable picturerate (informally also known as frame rate), of, for example 60 picturesper second or 60 Hz. Uncompressed video has significant bitraterequirements. For example, 1080p60 4:2:0 video at 8 bit per sample(1920×1080 luminance sample resolution at 60 Hz frame rate) requiresclose to 1.5 Gbit/s bandwidth. An hour of such video requires more than600 gigabytes (GB) of storage space.

One purpose of video coding and decoding can be the reduction ofredundancy in the input video signal, through compression. Compressioncan help reduce the aforementioned bandwidth or storage spacerequirements, in some cases by two orders of magnitude or more. Bothlossless and lossy compression, as well as a combination thereof can beemployed. Lossless compression refers to techniques where an exact copyof the original signal can be reconstructed from the compressed originalsignal. When using lossy compression, the reconstructed signal may notbe identical to the original signal, but the distortion between originaland reconstructed signals is small enough to make the reconstructedsignal useful for the intended application. In the case of video, lossycompression is widely employed. The amount of distortion tolerateddepends on the application; for example, users of certain consumerstreaming applications may tolerate higher distortion than users oftelevision distribution applications. The compression ratio achievablecan reflect that: higher allowable/tolerable distortion can yield highercompression ratios.

A video encoder and decoder can utilize techniques from several broadcategories, including, for example, motion compensation, transform,quantization, and entropy coding.

Video codec technologies can include techniques known as intra coding.In intra coding, sample values are represented without reference tosamples or other data from previously reconstructed reference pictures.In some video codecs, the picture is spatially subdivided into blocks ofsamples. When all blocks of samples are coded in intra mode, thatpicture can be an intra picture. Intra pictures and their derivationssuch as independent decoder refresh pictures, can be used to reset thedecoder state and can, therefore, be used as the first picture in acoded video bitstream and a video session, or as a still image. Thesamples of an intra block can be exposed to a transform, and thetransform coefficients can be quantized before entropy coding. Intraprediction can be a technique that minimizes sample values in thepre-transform domain. In some cases, the smaller the DC value after atransform is, and the smaller the AC coefficients are, the fewer thebits that are required at a given quantization step size to representthe block after entropy coding.

Traditional intra coding such as known from, for example MPEG-2generation coding technologies, does not use intra prediction. However,some newer video compression technologies include techniques thatattempt, from, for example, surrounding sample data and/or metadataobtained during the encoding/decoding of spatially neighboring, andpreceding in decoding order, blocks of data. Such techniques arehenceforth called “intra prediction” techniques. Note that in at leastsome cases, intra prediction is only using reference data from thecurrent picture under reconstruction and not from reference pictures.

There can be many different forms of intra prediction. When more thanone of such techniques can be used in a given video coding technology,the technique in use can be coded in an intra prediction mode. Incertain cases, modes can have submodes and/or parameters, and those canbe coded individually or included in the mode codeword. Which codewordto use for a given mode/submode/parameter combination can have an impactin the coding efficiency gain through intra prediction, and so can theentropy coding technology used to translate the codewords into abitstream.

A certain mode of intra prediction was introduced with H.264, refined inH.265, and further refined in newer coding technologies such as jointexploration model (JEM), versatile video coding (VVC), and benchmark set(BMS). A predictor block can be formed using neighboring sample valuesbelonging to already available samples. Sample values of neighboringsamples are copied into the predictor block according to a direction. Areference to the direction in use can be coded in the bitstream or mayitself be predicted.

SUMMARY

Aspects of the disclosure provide a modified implicit transform method.In addition, an implicit transform selection method for an interposition dependent prediction combination (PDPC) prediction mode isprovided.

According to an aspect of the disclosure, a method of video decoding fora decoder is provided. In the method, prediction information of acurrent block in a current picture is decoded from a coded videobitstream, where the prediction information is indicative of an interprediction mode. Whether a filtering process is applied on the currentblock is determined, where the filtering process adjusts interprediction samples of the current block based on neighboringreconstructed samples of the current block. A primary transform is thusperformed for a transform block according to a pre-defined primarytransform type based on that the filtering process is determined to beapplied on the current block, where the transform block is partitionedfrom the current block.

In some embodiments, the filtering process can be operated based on aposition dependent prediction combination (PDPC) mode or a combinedinter and intra prediction (CIIP) mode.

In some embodiments, the pre-defined primary transform type can be atype-7 discrete sine transform (DST-7) mode for a horizontal transformthat is applied to the transform block responsive to a width of thecurrent block being smaller than or equal to a threshold value. Thepre-defined primary transform type can be the DST-7 mode for a verticaltransform that is applied to the transform block responsive to a heightof the current block being smaller than or equal to the threshold value.The threshold value can include one of 4 pixels, 8 pixels, 16 pixels, or32 pixels.

In the method, the pre-defined primary transform type can be a type-2discrete cosine transform (DCT-2) mode for a horizontal transform thatis applied to the transform block responsive to a width of the currentblock being bigger than to a threshold value. The pre-defined primarytransform type can be the DCT-2 mode for a vertical transform is appliedto the transform block responsive to a height of the current block beinglarger than the threshold value. The threshold value can include one of4 pixels, 8 pixels, 16 pixels, or 32 pixels.

In some embodiments, the pre-defined primary transform type can be atransform skip mode (TSM), a DCT-2 mode, or a DST-7 mode.

In some embodiments, the filtering process can be a boundary filteringprocess in which at least one of rows adjacent to a boundary of thecurrent block or at least one of columns adjacent to the boundary of thecurrent block are adjusted based on the filtering process.

In some embodiments, the filtering process applies position-dependentweightings between the inter prediction samples of the current block andthe neighboring reconstructed samples of the current block.

In the method, the pre-defined primary transform type can be implicitfor a luma component of the current block, and a DCT-2 mode or atransform skip mode (TSM) for a chroma component of the current block.

In the method, the pre-defined primary transform type can be a type-7discrete sine transform (DST-7) mode for a horizontal transform that isapplied to the transform block responsive to (i) the filtering processbeing operated in the CIIP mode with a ratio of W_(intra)/W_(inter)being larger than a first threshold, and (ii) a width of the currentblock being smaller than or equal to a second threshold value. Theprimary transform type can be the DST-7 mode for a vertical transformthat is applied to the transform block responsive to (i) the filteringprocess being operated in the CIIP mode with the ratio ofW_(intra)/W_(inter) being larger than the first threshold, and (ii) aheight of the current block being smaller than or equal to the secondthreshold value. The first threshold value can include one of 2, 2.5, 3,or 7. The second threshold value can include one of 4 pixels, 8 pixels,16 pixels, or 32 pixels. W_(intra) can be an intra weighting factorapplied on an intra prediction information of the current block, andW_(inter) can be an inter weighting factor applied on an interprediction information of the current block.

In some embodiments, the pre-defined primary transform type can be atype-7 discrete sine transform (DST-7) mode for a horizontal transformthat is applied to the transform block responsive to (i) the filteringprocess being operated based on the CIIP mode, (ii) both above and leftneighboring blocks of the current block being intra coded, and (iii) awidth of the current block being smaller than or equal to a thresholdvalue. The pre-defined primary transform type can be the DST-7 mode fora vertical transform that is applied to the transform block responsiveto (i) the filtering process being operated in the CIIP mode, (ii) boththe above and the left neighboring blocks of the current block beingintra coded, and (ii) a height of the current block being smaller thanor equal to the threshold value. The threshold value can include one of4 pixels, 8 pixels, 16 pixels, or 32 pixels.

In some embodiments, the pre-defined primary transform type can be atype-7 discrete sine transform (DST-7) mode for a horizontal transformthat is applied to the transform block responsive to (i) the filteringprocess being operated based on the CIIP mode, (ii) a subset of aboveand left neighboring blocks of the current block being intra coded,(iii) a width of the current block being smaller than or equal to athreshold value. The pre-defined primary transform type can be the DST-7mode for a vertical transform that is applied to the transform blockresponsive to (i) the filtering process being operated based on the CIIPmode, (ii) the subset of the above and the left neighboring blocks ofthe current block being intra coded, and (iii) a height of the currentblock being smaller than or equal to the threshold value. The thresholdvalue can include one of 4 pixels, 8 pixels, 16 pixels, or 32 pixels.

In the method, a context model can be determined from a set of contextmodels based on the prediction information, where the predictioninformation indicates the filtering process that is based on the PDPCmode is applied to the current block. Primary transform type informationcan be decoded based on the determined context model, where the primarytransform type information indicates whether the pre-defined primarytransform type includes one of a transform skip mode (TSM), a DCT-2mode, a DST-7 mode, or a DCT-8 mode.

According to another aspect of the disclosure, a method of videodecoding for a decoder is provided. In the method, predictioninformation of a current block can be acquired from a coded videobitstream. A determination can be made as to whether the predictioninformation indicates (i) an inter prediction merge mode, and (ii) acombined inter and intra prediction (CIIP) mode. An intra predictionmode can be determined from an intra prediction mode candidate listresponsive to the prediction information indicating the inter predictionmerge mode and the CIIP mode. Intra prediction information according tothe intra prediction mode and inter prediction information according tothe inter prediction merge mode can be determined. A weighting factorcan further be determined responsive to neighboring blocks of thecurrent block being coded according to the CIIP mode or an interposition dependent prediction combination (PDPC) mode. CIIP predictioninformation can thus be determined based on a sum of a weighted intraprediction information and weighted inter prediction information, wherethe weighted intra prediction information is based on the intraprediction information and the weighting factor, and the weighted interprediction information is based on the inter prediction information andthe weighting factor. Further, a sample of the current block can bereconstructed according to the CIIP prediction information.

In some embodiments, weighted inter prediction information can be basedon the inter prediction information and a constant value minus theweighting factor, the constant value including one of 2, 4, 8, or 16.

In some embodiments, the weighting factor can be 3 responsive to bothtop-right/top and bottom-left/left neighboring blocks of the currentblock being coded using the CIIP mode. In some embodiment, the weightingfactor can be 2 responsive to one of the top-right/top and thebottom-left/left neighboring blocks of the current block being codedusing the CIIP mode. In some embodiments, the weighting factor can be 1responsive to the top-right/top and the bottom-left/left neighboringblocks of the current block being coded using the CIIP mode.

In some embodiments, the weighting factor can be 3 responsive to bothtop-right/top and bottom-left/left neighboring blocks of the currentblock being coded using the PDPC mode. The weighting factor can be 2responsive to one of the top-right/top and the bottom-left/leftneighboring blocks of the current block being coded using the PDPC mode.The weighting factor can be 1 responsive to none of the top-right/topand the bottom-left/left neighboring blocks of the current block beingcoded using the PDPC mode.

According to yet another aspect of the disclosure, a method of videodecoding for a decoder is provided. In the method, transform blocksignaling information can be acquired from a coded video bitstream,where the transform block signaling information includes firstinformation associated with an inter prediction transform and secondinformation associated with an intra prediction transform. A first valueof the first information and a second value of the second informationcan subsequently be determined. A first transform block coded in aninter prediction mode can be transformed according to the first valueand a first pre-defined transform type in an implicit multiple transformselection (MTS) mode. A second transform block coded in an intraprediction mode can be transformed according to a second value and asecond pre-defined transform type in the implicit MTS mode.

In some embodiments, the first value of the first information can beequal to 1 and the second value of the second information can be equalto 1.

In some embodiments, the first value of the first information can begreater than 0, and the second value of the second information can beequal to 1.

In some embodiments, the second transform block coded in the intraprediction mode can be transformed according to the second value, thesecond pre-defined transform type in the implicit MTS mode, and a codingunit that includes the second transform block being intrasub-partitioning (ISP) coded. The second value is larger than 0.

Aspects of the disclosure also provide a non-transitorycomputer-readable medium storing instructions which when executed by acomputer for video decoding cause the computer to perform any one or acombination of the methods for video decoding.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, the nature, and various advantages of the disclosedsubject matter will be more apparent from the following detaileddescription and the accompanying drawings in which:

FIG. 1 is a schematic illustration of a simplified block diagram of acommunication system (100) in accordance with an embodiment.

FIG. 2 is a schematic illustration of a simplified block diagram of acommunication system (200) in accordance with an embodiment.

FIG. 3 is a schematic illustration of a simplified block diagram of adecoder in accordance with an embodiment.

FIG. 4 is a schematic illustration of a simplified block diagram of anencoder in accordance with an embodiment.

FIG. 5 shows a block diagram of an encoder in accordance with anotherembodiment.

FIG. 6 shows a block diagram of a decoder in accordance with anotherembodiment.

FIGS. 7A-7D show four exemplary sub-block transform modes.

FIG. 8 shows a first exemplary division of a luma intra-predicted blockbased on Intra Sub-Partitions (ISP) coding mode.

FIG. 9 shows a second exemplary division of a luma intra-predicted blockbased on ISP coding mode.

FIG. 10 shows an example of reduced secondary transform (RST) using a16×64 secondary transform core.

FIG. 11 shows an example of RST using a 16×48 secondary transform core.

FIG. 12A shows an example of a forward reduced transform.

FIG. 12B shows an example of an inverse reduced transform.

FIG. 13A shows a first embodiment of RST8×8.

FIG. 13B shows a second embodiment of RST8×8.

FIG. 14 shows a Matrix-based intra prediction (MIP) mode.

FIG. 15 shows 35 intra prediction modes in accordance with anembodiment.

FIG. 16 shows 95 intra prediction modes in accordance with anembodiment.

FIG. 17A shows a first example of position dependent predictioncombination (PDPC) weights in accordance with an embodiment.

FIG. 17B shows a second example of PDPC weights in accordance with anembodiment.

FIG. 18A shows a first example of triangle partition based interprediction.

FIG. 18B shows a second example of triangle partition based interprediction.

FIG. 19 shows a flow chart outlining a first process example accordingto some embodiments of the disclosure.

FIG. 20 shows a flow chart outlining a second process example accordingto some embodiments of the disclosure.

FIG. 21 shows a flow chart outlining a third process example accordingto some embodiments of the disclosure.

FIG. 22 is a schematic illustration of a computer system in accordancewith an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 illustrates a simplified block diagram of a communication system(100) according to an embodiment of the present disclosure. Thecommunication system (100) includes a plurality of terminal devices thatcan communicate with each other, via, for example, a network (150). Forexample, the communication system (100) includes a first pair ofterminal devices (110) and (120) interconnected via the network (150).In the FIG. 1 example, the first pair of terminal devices (110) and(120) performs unidirectional transmission of data. For example, theterminal device (110) may code video data (e.g., a stream of videopictures that are captured by the terminal device (110)) fortransmission to the other terminal device (120) via the network (150).The encoded video data can be transmitted in the form of one or morecoded video bitstreams. The terminal device (120) may receive the codedvideo data from the network (150), decode the coded video data torecover the video pictures and display video pictures according to therecovered video data. Unidirectional data transmission may be common inmedia serving applications and the like.

In another example, the communication system (100) includes a secondpair of terminal devices (130) and (140) that performs bidirectionaltransmission of coded video data that may occur, for example, duringvideoconferencing. For bidirectional transmission of data, in anexample, each terminal device of the terminal devices (130) and (140)may code video data (e.g., a stream of video pictures that are capturedby the terminal device) for transmission to the other terminal device ofthe terminal devices (130) and (140) via the network (150). Eachterminal device of the terminal devices (130) and (140) also may receivethe coded video data transmitted by the other terminal device of theterminal devices (130) and (140), and may decode the coded video data torecover the video pictures and may display video pictures at anaccessible display device according to the recovered video data.

In the FIG. 1 example, the terminal devices (110), (120), (130) and(140) may be illustrated as servers, personal computers and smart phonesbut the principles of the present disclosure may be not so limited.Embodiments of the present disclosure find application with laptopcomputers, tablet computers, media players and/or dedicated videoconferencing equipment. The network (150) represents any number ofnetworks that convey coded video data among the terminal devices (110),(120), (130) and (140), including for example wireline (wired) and/orwireless communication networks. The communication network (150) mayexchange data in circuit-switched and/or packet-switched channels.Representative networks include telecommunications networks, local areanetworks, wide area networks and/or the Internet. For the purposes ofthe present discussion, the architecture and topology of the network(150) may be immaterial to the operation of the present disclosureunless explained herein below.

FIG. 2 illustrates, as an example for an application for the disclosedsubject matter, the placement of a video encoder and a video decoder ina streaming environment. The disclosed subject matter can be equallyapplicable to other video enabled applications, including, for example,video conferencing, digital TV, storing of compressed video on digitalmedia including CD, DVD, memory stick and the like, and so on.

A streaming system may include a capture subsystem (213), that caninclude a video source (201), for example a digital camera, creating forexample a stream of video pictures (202) that are uncompressed. In anexample, the stream of video pictures (202) includes samples that aretaken by the digital camera. The stream of video pictures (202),depicted as a bold line to emphasize a high data volume when compared toencoded video data (204) (or coded video bitstreams), can be processedby an electronic device (220) that includes a video encoder (203)coupled to the video source (201). The video encoder (203) can includehardware, software, or a combination thereof to enable or implementaspects of the disclosed subject matter as described in more detailbelow. The encoded video data (204) (or encoded video bitstream (204)),depicted as a thin line to emphasize the lower data volume when comparedto the stream of video pictures (202), can be stored on a streamingserver (205) for future use. One or more streaming client subsystems,such as client subsystems (206) and (208) in FIG. 2 can access thestreaming server (205) to retrieve copies (207) and (209) of the encodedvideo data (204). A client subsystem (206) can include a video decoder(210), for example, in an electronic device (230). The video decoder(210) decodes the incoming copy (207) of the encoded video data andcreates an outgoing stream of video pictures (211) that can be renderedon a display (212) (e.g., display screen) or other rendering device (notdepicted). In some streaming systems, the encoded video data (204),(207), and (209) (e.g., video bitstreams) can be encoded according tocertain video coding/compression standards. Examples of those standardsinclude ITU-T Recommendation H.265. In an example, a video codingstandard under development is informally known as Versatile Video Coding(VVC). The disclosed subject matter may be used in the context of VVC.

It is noted that the electronic devices (220) and (230) can includeother components (not shown). For example, the electronic device (220)can include a video decoder (not shown) and the electronic device (230)can include a video encoder (not shown) as well.

FIG. 3 shows a block diagram of a video decoder (310) according to anembodiment of the present disclosure. The video decoder (310) can beincluded in an electronic device (330). The electronic device (330) caninclude a receiver (331) (e.g., receiving circuitry). The video decoder(310) can be used in the place of the video decoder (210) in the FIG. 2example.

The receiver (331) may receive one or more coded video sequences to bedecoded by the video decoder (310); in the same or another embodiment,one coded video sequence at a time, where the decoding of each codedvideo sequence is independent from other coded video sequences. Thecoded video sequence may be received from a channel (301), which may bea hardware/software link to a storage device which stores the encodedvideo data. The receiver (331) may receive the encoded video data withother data, for example, coded audio data and/or ancillary data streams,that may be forwarded to their respective using entities (not depicted).The receiver (331) may separate the coded video sequence from the otherdata. To combat network jitter, a buffer memory (315) may be coupled inbetween the receiver (331) and an entropy decoder/parser (320) (“parser(320)” henceforth). In certain applications, the buffer memory (315) ispart of the video decoder (310). In others, it can be outside of thevideo decoder (310) (not depicted). Instill others, there can be abuffer memory (not depicted) outside of the video decoder (310), forexample to combat network jitter, and in addition another buffer memory(315) inside the video decoder (310), for example to handle playouttiming. When the receiver (331) is receiving data from a store/forwarddevice of sufficient bandwidth and controllability, or from anisosynchronous network, the buffer memory (315) may not be needed, orcan be small. For use on best effort packet networks such as theInternet, the buffer memory (315) may be required, can be comparativelylarge and can be advantageously of adaptive size, and may at leastpartially be implemented in an operating system or similar elements (notdepicted) outside of the video decoder (310).

The video decoder (310) may include the parser (320) to reconstructsymbols (321) from the coded video sequence. Categories of those symbolsinclude information used to manage operation of the video decoder (310),and potentially information to control a rendering device such as arender device (312) (e.g., a display screen) that is not an integralpart of the electronic device (330) but can be coupled to the electronicdevice (330), as was shown in FIG. 3. The control information for therendering device(s) may be in the form of Supplemental EnhancementInformation (SEI messages) or Video Usability Information (VUI)parameter set fragments (not depicted). The parser (320) mayparse/entropy-decode the coded video sequence that is received. Thecoding of the coded video sequence can be in accordance with a videocoding technology or standard, and can follow various principles,including variable length coding, Huffman coding, arithmetic coding withor without context sensitivity, and so forth. The parser (320) mayextract from the coded video sequence, a set of subgroup parameters forat least one of the subgroups of pixels in the video decoder, based uponat least one parameter corresponding to the group. Subgroups can includeGroups of Pictures (GOPs), pictures, tiles, slices, macroblocks, CodingUnits (CUs), blocks, Transform Units (TUs), Prediction Units (PUs) andso forth. The parser (320) may also extract from the coded videosequence information such as transform coefficients, quantizer parametervalues, motion vectors, and so forth.

The parser (320) may perform an entropy decoding/parsing operation onthe video sequence received from the buffer memory (315), so as tocreate symbols (321).

Reconstruction of the symbols (321) can involve multiple different unitsdepending on the type of the coded video picture or parts thereof (suchas: inter and intra picture, inter and intra block), and other factors.Which units are involved, and how, can be controlled by the subgroupcontrol information that was parsed from the coded video sequence by theparser (320). The flow of such subgroup control information between theparser (320) and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, the video decoder (310)can be conceptually subdivided into a number of functional units asdescribed below. In a practical implementation operating undercommercial constraints, many of these units interact closely with eachother and can, at least partly, be integrated into each other. However,for the purpose of describing the disclosed subject matter, theconceptual subdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit (351). Thescaler/inverse transform unit (351) receives a quantized transformcoefficient as well as control information, including which transform touse, block size, quantization factor, quantization scaling matrices,etc. as symbol(s) (321) from the parser (320). The scaler/inversetransform unit (351) can output blocks comprising sample values, thatcan be input into aggregator (355).

In some cases, the output samples of the scaler/inverse transform (351)can pertain to an intra coded block; that is: a block that is not usingpredictive information from previously reconstructed pictures, but canuse predictive information from previously reconstructed parts of thecurrent picture. Such predictive information can be provided by an intrapicture prediction unit (352). In some cases, the intra pictureprediction unit (352) generates a block of the same size and shape ofthe block under reconstruction, using surrounding already reconstructedinformation fetched from the current picture buffer (358). The currentpicture buffer (358) buffers, for example, partly reconstructed currentpicture and/or fully reconstructed current picture. The aggregator(355), in some cases, adds, on a per sample basis, the predictioninformation the intra prediction unit (352) has generated to the outputsample information as provided by the scaler/inverse transform unit(351).

In other cases, the output samples of the scaler/inverse transform unit(351) can pertain to an inter coded, and potentially motion compensatedblock. In such a case, a motion compensation prediction unit (353) canaccess reference picture memory (357) to fetch samples used forprediction. After motion compensating the fetched samples in accordancewith the symbols (321) pertaining to the block, these samples can beadded by the aggregator (355) to the output of the scaler/inversetransform unit (351) (in this case called the residual samples orresidual signal) so as to generate output sample information. Theaddresses within the reference picture memory (357) from where themotion compensation prediction unit (353) fetches prediction samples canbe controlled by motion vectors, available to the motion compensationprediction unit (353) in the form of symbols (321) that can have, forexample X, Y, and reference picture components. Motion compensation alsocan include interpolation of sample values as fetched from the referencepicture memory (357) when sub-sample exact motion vectors are in use,motion vector prediction mechanisms, and so forth.

The output samples of the aggregator (355) can be subject to variousloop filtering techniques in the loop filter unit (356). Videocompression technologies can include in-loop filter technologies thatare controlled by parameters included in the coded video sequence (alsoreferred to as coded video bitstream) and made available to the loopfilter unit (356) as symbols (321) from the parser (320), but can alsobe responsive to meta-information obtained during the decoding ofprevious (in decoding order) parts of the coded picture or coded videosequence, as well as responsive to previously reconstructed andloop-filtered sample values.

The output of the loop filter unit (356) can be a sample stream that canbe output to the render device (312) as well as stored in the referencepicture memory (357) for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used asreference pictures for future prediction. For example, once a codedpicture corresponding to a current picture is fully reconstructed andthe coded picture has been identified as a reference picture (by, forexample, the parser (320)), the current picture buffer (358) can becomea part of the reference picture memory (357), and a fresh currentpicture buffer can be reallocated before commencing the reconstructionof the following coded picture.

The video decoder (310) may perform decoding operations according to apredetermined video compression technology in a standard, such as ITU-TRec. H.265. The coded video sequence may conform to a syntax specifiedby the video compression technology or standard being used, in the sensethat the coded video sequence adheres to both the syntax of the videocompression technology or standard and the profiles as documented in thevideo compression technology or standard. Specifically, a profile canselect certain tools as the only tools available for use under thatprofile from all the tools available in the video compression technologyor standard. Also necessary for compliance can be that the complexity ofthe coded video sequence is within bounds as defined by the level of thevideo compression technology or standard. In some cases, levels restrictthe maximum picture size, maximum frame rate, maximum reconstructionsample rate (measured in, for example megasamples per second), maximumreference picture size, and so on. Limits set by levels can, in somecases, be further restricted through Hypothetical Reference Decoder(HRD) specifications and metadata for HRD buffer management signaled inthe coded video sequence.

In an embodiment, the receiver (331) may receive additional (redundant)data with the encoded video. The additional data may be included as partof the coded video sequence(s). The additional data may be used by thevideo decoder (310) to properly decode the data and/or to moreaccurately reconstruct the original video data. Additional data can bein the form of, for example, temporal, spatial, or signal noise ratio(SNR) enhancement layers, redundant slices, redundant pictures, forwarderror correction codes, and so on.

FIG. 4 shows a block diagram of a video encoder (403) according to anembodiment of the present disclosure. The video encoder (403) isincluded in an electronic device (420). The electronic device (420)includes a transmitter (440) (e.g., transmitting circuitry). The videoencoder (403) can be used in the place of the video encoder (203) in theFIG. 2 example.

The video encoder (403) may receive video samples from a video source(401) (that is not part of the electronic device (420) in the FIG. 4example) that may capture video image(s) to be coded by the videoencoder (403). In another example, the video source (401) is a part ofthe electronic device (420).

The video source (401) may provide the source video sequence to be codedby the video encoder (403) in the form of a digital video sample streamthat can be of any suitable bit depth (for example: 8 bit, 10 bit, 12bit, . . . ), any colorspace (for example, BT.601 Y CrCB, RGB, . . . ),and any suitable sampling structure (for example Y CrCb 4:2:0, Y CrCb4:4:4). In a media serving system, the video source (401) may be astorage device storing previously prepared video. In a videoconferencingsystem, the video source (401) may be a camera that captures local imageinformation as a video sequence. Video data may be provided as aplurality of individual pictures that impart motion when viewed insequence. The pictures themselves may be organized as a spatial array ofpixels, wherein each pixel can comprise one or more samples depending onthe sampling structure, color space, etc. in use. A person skilled inthe art can readily understand the relationship between pixels andsamples. The description below focuses on samples.

According to an embodiment, the video encoder (403) may code andcompress the pictures of the source video sequence into a coded videosequence (443) in real time or under any other time constraints asrequired by the application. Enforcing appropriate coding speed is onefunction of a controller (450). In some embodiments, the controller(450) controls other functional units as described below and isfunctionally coupled to the other functional units. The coupling is notdepicted for clarity. Parameters set by the controller (450) can includerate control related parameters (picture skip, quantizer, lambda valueof rate-distortion optimization techniques, . . . ), picture size, groupof pictures (GOP) layout, maximum motion vector search range, and soforth. The controller (450) can be configured to have other suitablefunctions that pertain to the video encoder (403) optimized for acertain system design.

In some embodiments, the video encoder (403) is configured to operate ina coding loop. As an oversimplified description, in an example, thecoding loop can include a source coder (430) (e.g., responsible forcreating symbols, such as a symbol stream, based on an input picture tobe coded, and a reference picture(s)), and a (local) decoder (433)embedded in the video encoder (403). The decoder (433) reconstructs thesymbols to create the sample data in a similar manner as a (remote)decoder also would create (as any compression between symbols and codedvideo bitstream is lossless in the video compression technologiesconsidered in the disclosed subject matter). The reconstructed samplestream (sample data) is input to the reference picture memory (434). Asthe decoding of a symbol stream leads to bit-exact results independentof decoder location (local or remote), the content in the referencepicture memory (434) is also bit exact between the local encoder andremote encoder. In other words, the prediction part of an encoder “sees”as reference picture samples exactly the same sample values as a decoderwould “see” when using prediction during decoding. This fundamentalprinciple of reference picture synchronicity (and resulting drift, ifsynchronicity cannot be maintained, for example because of channelerrors) is used in some related arts as well.

The operation of the “local” decoder (433) can be the same as of a“remote” decoder, such as the video decoder (310), which has alreadybeen described in detail above in conjunction with FIG. 3. Brieflyreferring also to FIG. 3, however, as symbols are available andencoding/decoding of symbols to a coded video sequence by an entropycoder (445) and the parser (320) can be lossless, the entropy decodingparts of the video decoder (310), including the buffer memory (315), andparser (320) may not be fully implemented in the local decoder (433).

An observation that can be made at this point is that any decodertechnology except the parsing/entropy decoding that is present in adecoder also necessarily needs to be present, in substantially identicalfunctional form, in a corresponding encoder. For this reason, thedisclosed subject matter focuses on decoder operation. The descriptionof encoder technologies can be abbreviated as they are the inverse ofthe comprehensively described decoder technologies. Only in certainareas a more detail description is required and provided below.

During operation, in some examples, the source coder (430) may performmotion compensated predictive coding, which codes an input picturepredicatively with reference to one or more previously-coded picturefrom the video sequence that were designated as “reference pictures”. Inthis manner, the coding engine (432) codes differences between pixelblocks of an input picture and pixel blocks of reference picture(s) thatmay be selected as prediction reference(s) to the input picture.

The local video decoder (433) may decode coded video data of picturesthat may be designated as reference pictures, based on symbols createdby the source coder (430). Operations of the coding engine (432) mayadvantageously be lossy processes. When the coded video data may bedecoded at a video decoder (not shown in FIG. 4), the reconstructedvideo sequence typically may be a replica of the source video sequencewith some errors. The local video decoder (433) replicates decodingprocesses that may be performed by the video decoder on referencepictures and may cause reconstructed reference pictures to be stored inthe reference picture cache (434). In this manner, the video encoder(403) may store copies of reconstructed reference pictures locally thathave common content as the reconstructed reference pictures that will beobtained by a far-end video decoder (absent transmission errors).

The predictor (435) may perform prediction searches for the codingengine (432). That is, for a new picture to be coded, the predictor(435) may search the reference picture memory (434) for sample data (ascandidate reference pixel blocks) or certain metadata such as referencepicture motion vectors, block shapes, and so on, that may serve as anappropriate prediction reference for the new pictures. The predictor(435) may operate on a sample block-by-pixel block basis to findappropriate prediction references. In some cases, as determined bysearch results obtained by the predictor (435), an input picture mayhave prediction references drawn from multiple reference pictures storedin the reference picture memory (434).

The controller (450) may manage coding operations of the source coder(430), including, for example, setting of parameters and subgroupparameters used for encoding the video data.

Output of all aforementioned functional units may be subjected toentropy coding in the entropy coder (445). The entropy coder (445)translates the symbols as generated by the various functional units intoa coded video sequence, by lossless compressing the symbols according totechnologies such as Huffman coding, variable length coding, arithmeticcoding, and so forth.

The transmitter (440) may buffer the coded video sequence(s) as createdby the entropy coder (445) to prepare for transmission via acommunication channel (460), which may be a hardware/software link to astorage device which would store the encoded video data. The transmitter(440) may merge coded video data from the video coder (403) with otherdata to be transmitted, for example, coded audio data and/or ancillarydata streams (sources not shown).

The controller (450) may manage operation of the video encoder (403).During coding, the controller (450) may assign to each coded picture acertain coded picture type, which may affect the coding techniques thatmay be applied to the respective picture. For example, pictures oftenmay be assigned as one of the following picture types:

An Intra Picture (I picture) may be one that may be coded and decodedwithout using any other picture in the sequence as a source ofprediction. Some video codecs allow for different types of intrapictures, including, for example Independent Decoder Refresh (“IDR”)Pictures. A person skilled in the art is aware of those variants of Ipictures and their respective applications and features.

A predictive picture (P picture) may be one that may be coded anddecoded using intra prediction or inter prediction using at most onemotion vector and reference index to predict the sample values of eachblock.

A bi-directionally predictive picture (B Picture) may be one that may becoded and decoded using intra prediction or inter prediction using atmost two motion vectors and reference indices to predict the samplevalues of each block. Similarly, multiple-predictive pictures can usemore than two reference pictures and associated metadata for thereconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality ofsample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 sampleseach) and coded on a block-by-block basis. Blocks may be codedpredicatively with reference to other (already coded) blocks asdetermined by the coding assignment applied to the blocks' respectivepictures. For example, blocks of I pictures may be codednon-predicatively or they may be coded predicatively with reference toalready coded blocks of the same picture (spatial prediction or intraprediction). Pixel blocks of P pictures may be coded predicatively, viaspatial prediction or via temporal prediction with reference to onepreviously coded reference picture. Blocks of B pictures may be codedpredicatively, via spatial prediction or via temporal prediction withreference to one or two previously coded reference pictures.

The video encoder (403) may perform coding operations according to apredetermined video coding technology or standard, such as ITU-T Rec.H.265. In its operation, the video encoder (403) may perform variouscompression operations, including predictive coding operations thatexploit temporal and spatial redundancies in the input video sequence.The coded video data, therefore, may conform to a syntax specified bythe video coding technology or standard being used.

In an embodiment, the transmitter (440) may transmit additional datawith the encoded video. The source coder (430) may include such data aspart of the coded video sequence. Additional data may comprisetemporal/spatial/SNR enhancement layers, other forms of redundant datasuch as redundant pictures and slices, SEI messages, VUI parameter setfragments, and so on.

A video may be captured as a plurality of source pictures (videopictures) in a temporal sequence. Intra-picture prediction (oftenabbreviated to intra prediction) makes use of spatial correlation in agiven picture, and inter-picture prediction makes uses of the (temporalor other) correlation between the pictures. In an example, a specificpicture under encoding/decoding, which is referred to as a currentpicture, is partitioned into blocks. When a block in the current pictureis similar to a reference block in a previously coded and still bufferedreference picture in the video, the block in the current picture can becoded by a vector that is referred to as a motion vector. The motionvector points to the reference block in the reference picture, and canhave a third dimension identifying the reference picture, in casemultiple reference pictures are in use.

In some embodiments, a bi-prediction technique can be used in theinter-picture prediction. According to the bi-prediction technique, tworeference pictures, such as a first reference picture and a secondreference picture that are both prior in decoding order to the currentpicture in the video (but may be in the past and future, respectively,in display order) are used. A block in the current picture can be codedby a first motion vector that points to a first reference block in thefirst reference picture, and a second motion vector that points to asecond reference block in the second reference picture. The block can bepredicted by a combination of the first reference block and the secondreference block.

Further, a merge mode technique can be used in the inter-pictureprediction to improve coding efficiency.

According to some embodiments of the disclosure, predictions, such asinter-picture predictions and intra-picture predictions are performed inthe unit of blocks. For example, according to the HEVC standard, apicture in a sequence of video pictures is partitioned into coding treeunits (CTU) for compression, the CTUs in a picture have the same size,such as 64×64 pixels, 32×32 pixels, or 16×16 pixels. In general, a CTUincludes three coding tree blocks (CTBs), which are one luma CTB and twochroma CTBs. Each CTU can be recursively quadtree split into one ormultiple coding units (CUs). For example, a CTU of 64×64 pixels can besplit into one CU of 64×64 pixels, or 4 CUs of 32×32 pixels, or 16 CUsof 16×16 pixels. In an example, each CU is analyzed to determine aprediction type for the CU, such as an inter prediction type or an intraprediction type. The CU is split into one or more prediction units (PUs)depending on the temporal and/or spatial predictability. Generally, eachPU includes a luma prediction block (PB), and two chroma PBs. In anembodiment, a prediction operation in coding (encoding/decoding) isperformed in the unit of a prediction block. Using a luma predictionblock as an example of a prediction block, the prediction block includesa matrix of values (e.g., luma values) for pixels, such as 8×8 pixels,16×16 pixels, 8×16 pixels, 16×8 pixels, and the like.

FIG. 5 shows a diagram of a video encoder (503) according to anotherembodiment of the disclosure. The video encoder (503) is configured toreceive a processing block (e.g., a prediction block) of sample valueswithin a current video picture in a sequence of video pictures, andencode the processing block into a coded picture that is part of a codedvideo sequence. In an example, the video encoder (503) is used in theplace of the video encoder (203) in the FIG. 2 example.

In an HEVC example, the video encoder (503) receives a matrix of samplevalues for a processing block, such as a prediction block of 8×8samples, and the like. The video encoder (503) determines whether theprocessing block is best coded using intra mode, inter mode, orbi-prediction mode using, for example, rate-distortion optimization.When the processing block is to be coded in intra mode, the videoencoder (503) may use an intra prediction technique to encode theprocessing block into the coded picture; and when the processing blockis to be coded in inter mode or bi-prediction mode, the video encoder(503) may use an inter prediction or bi-prediction technique,respectively, to encode the processing block into the coded picture. Incertain video coding technologies, merge mode can be an inter pictureprediction submode where the motion vector is derived from one or moremotion vector predictors without the benefit of a coded motion vectorcomponent outside the predictors. In certain other video codingtechnologies, a motion vector component applicable to the subject blockmay be present. In an example, the video encoder (503) includes othercomponents, such as a mode decision module (not shown) to determine themode of the processing blocks.

In the FIG. 5 example, the video encoder (503) includes the interencoder (530), an intra encoder (522), a residue calculator (523), aswitch (526), a residue encoder (524), a general controller (521), andan entropy encoder (525) coupled together as shown in FIG. 5.

The inter encoder (530) is configured to receive the samples of thecurrent block (e.g., a processing block), compare the block to one ormore reference blocks in reference pictures (e.g., blocks in previouspictures and later pictures), generate inter prediction information(e.g., description of redundant information according to inter encodingtechnique, motion vectors, merge mode information), and calculate interprediction results (e.g., predicted block) based on the inter predictioninformation using any suitable technique. In some examples, thereference pictures are decoded reference pictures that are decoded basedon the encoded video information.

The intra encoder (522) is configured to receive the samples of thecurrent block (e.g., a processing block), in some cases compare theblock to blocks already coded in the same picture, generate quantizedcoefficients after transform, and in some cases also intra predictioninformation (e.g., an intra prediction direction information accordingto one or more intra encoding techniques). In an example, the intraencoder (522) also calculates intra prediction results (e.g., predictedblock) based on the intra prediction information and reference blocks inthe same picture.

The general controller (521) is configured to determine general controldata and control other components of the video encoder (503) based onthe general control data. In an example, the general controller (521)determines the mode of the block, and provides a control signal to theswitch (526) based on the mode. For example, when the mode is the intramode, the general controller (521) controls the switch (526) to selectthe intra mode result for use by the residue calculator (523), andcontrols the entropy encoder (525) to select the intra predictioninformation and include the intra prediction information in thebitstream; and when the mode is the inter mode, the general controller(521) controls the switch (526) to select the inter prediction resultfor use by the residue calculator (523), and controls the entropyencoder (525) to select the inter prediction information and include theinter prediction information in the bitstream.

The residue calculator (523) is configured to calculate a difference(residue data) between the received block and prediction resultsselected from the intra encoder (522) or the inter encoder (530). Theresidue encoder (524) is configured to operate based on the residue datato encode the residue data to generate the transform coefficients. In anexample, the residue encoder (524) is configured to convert the residuedata from a spatial domain to a frequency domain, and generate thetransform coefficients. The transform coefficients are then subject toquantization processing to obtain quantized transform coefficients. Invarious embodiments, the video encoder (503) also includes a residuedecoder (528). The residue decoder (528) is configured to performinverse-transform, and generate the decoded residue data. The decodedresidue data can be suitably used by the intra encoder (522) and theinter encoder (530). For example, the inter encoder (530) can generatedecoded blocks based on the decoded residue data and inter predictioninformation, and the intra encoder (522) can generate decoded blocksbased on the decoded residue data and the intra prediction information.The decoded blocks are suitably processed to generate decoded picturesand the decoded pictures can be buffered in a memory circuit (not shown)and used as reference pictures in some examples.

The entropy encoder (525) is configured to format the bitstream toinclude the encoded block. The entropy encoder (525) is configured toinclude various information according to a suitable standard, such asthe HEVC standard. In an example, the entropy encoder (525) isconfigured to include the general control data, the selected predictioninformation (e.g., intra prediction information or inter predictioninformation), the residue information, and other suitable information inthe bitstream. Note that, according to the disclosed subject matter,when coding a block in the merge submode of either inter mode orbi-prediction mode, there is no residue information.

FIG. 6 shows a diagram of a video decoder (610) according to anotherembodiment of the disclosure. The video decoder (610) is configured toreceive coded pictures that are part of a coded video sequence, anddecode the coded pictures to generate reconstructed pictures. In anexample, the video decoder (610) is used in the place of the videodecoder (210) in the FIG. 2 example.

In the FIG. 6 example, the video decoder (610) includes an entropydecoder (671), an inter decoder (680), a residue decoder (673), areconstruction module (674), and an intra decoder (672) coupled togetheras shown in FIG. 6.

The entropy decoder (671) can be configured to reconstruct, from thecoded picture, certain symbols that represent the syntax elements ofwhich the coded picture is made up. Such symbols can include, forexample, the mode in which a block is coded (such as, for example, intramode, inter mode, bi-predicted mode, the latter two in merge submode oranother submode), prediction information (such as, for example, intraprediction information or inter prediction information) that canidentify certain sample or metadata that is used for prediction by theintra decoder (672) or the inter decoder (680), respectively, residualinformation in the form of, for example, quantized transformcoefficients, and the like. In an example, when the prediction mode isinter or bi-predicted mode, the inter prediction information is providedto the inter decoder (680); and when the prediction type is the intraprediction type, the intra prediction information is provided to theintra decoder (672). The residual information can be subject to inversequantization and is provided to the residue decoder (673).

The inter decoder (680) is configured to receive the inter predictioninformation, and generate inter prediction results based on the interprediction information.

The intra decoder (672) is configured to receive the intra predictioninformation, and generate prediction results based on the intraprediction information.

The residue decoder (673) is configured to perform inverse quantizationto extract de-quantized transform coefficients, and process thede-quantized transform coefficients to convert the residual from thefrequency domain to the spatial domain. The residue decoder (673) mayalso require certain control information (to include the QuantizerParameter (QP)), and that information may be provided by the entropydecoder (671)(data path not depicted as this may be low volume controlinformation only).

The reconstruction module (674) is configured to combine, in the spatialdomain, the residual as output by the residue decoder (673) and theprediction results (as output by the inter or intra prediction modulesas the case may be) to form a reconstructed block, that may be part ofthe reconstructed picture, which in turn may be part of thereconstructed video. It is noted that other suitable operations, such asa deblocking operation and the like, can be performed to improve thevisual quality.

It is noted that the video encoders (203), (403), and (503), and thevideo decoders (210), (310), and (610) can be implemented using anysuitable technique. In an embodiment, the video encoders (203), (403),and (503), and the video decoders (210), (310), and (610) can beimplemented using one or more integrated circuits. In anotherembodiment, the video encoders (203), (403), and (403), and the videodecoders (210), (310), and (610) can be implemented using one or moreprocessors that execute software instructions.

Primary transforms, such as in HEVC, can include 4-point, 8-point,16-point, and 32-point type-2 discrete cosine transform (DCT-2), and thetransform core matrices can be represented using 8-bit integers, i.e.,8-bit transform core. The transform core matrices of smaller DCT-2transforms can be part of larger DCT-2, transforms as shown below.

  4 × 4 transform   {64, 64, 64, 64}   {83, 36, −36, −83}   {64, −64,−64, 64}   {36, −83, 83, −36} 8 × 8 transform   {64, 64, 64, 64, 64, 64,64, 64}   {89, 75, 50, 18, −18, −50, −75, −39}   {83, 36, −36, −83, −33,−36, 36, 83}   {75, −18, −89, −50, 50, 89, 18, −75}   {64, −64, −64, 64,64, −64, −64, 64}   {50, −89, 18, 75, −75, −18, 89, −50}   {36, −83, 83,−36, −36, 83, −83, 36}   {18, −50, 75, −89, 89, −75, 50, −18} 16 × 16transform   {64 64 64 66 64 64 64 64 64 64 64 64 64 64 64 64}   {90 8780 70 57 43 25 9 −9−25−43−57−70−80−87−90}   {89 75 5018−18−50−75−89−89−75−50−18 18 50 75 89}   {87 57 9−43−80−90−70−25 25 7090 80 43 −9−57−87}   {83 36−36−83−83−36 36 83 83 36−36−33 83−36 36 83}  {80 9−70−87−25 57 90 43−43−90−57 25 87 70 −9−80}   {75−18−89−50 50 8918−75−75 18 89 50−50−89−18 75}   {70−43−87 9 90 25−80−57 57 80−25−90 −987 43−70}   {64−64−64 64 64−64−64 64 64−64−64 64 64−64−64 64}  {57−80−25 90 −9−87 43 70−70−43 87 9−90 25 80−57}   {50−89 18 75−75−1889−50−50 89−18−75 75 18−89 50}   {43−90 57 25−87 70 9−80 80 −9−7087−25−57 90−43}   {36−83 83−36−36 83−83 36 36−83 83−36−36 83−83 36}  {25 −70 90−80 43 9−57 87−87 57 −9−43 80−90 70−25}   {18−50 75−89 89−7550−18−18 50−75 89−89 75−50 18}   { 9−25 43−57 70−80 87−90 90−87 80−7057−43 25 −9} 32 × 32 transform {64 64 64 64 64 64 64 64 64 64 64 64 6464 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64} {90 90 88 8582 78 73 67 61 54 46 38 31 22 13 4 −4−13−22−31−38−46−54−61−67−73−78−82−85−88−90−90} {90 87 80 70 57 43 25 9−9−25−43−57−70−80−87−90−90 −87−80−70−57−43−25 −9 9 25 43 57 70 80 87 90}{90 82 67 46 22 −4−31−54−73−85−90−88−78−61−38−13 13 38 61 78 88 90 85 7354 31 4−22−46−67−82−90} {39 75 50 18−18−50−75 −89−89−75−50−18 18 50 7589 89 75 50 18−18−50−75−89−89−75−50−18 18 50 75 89} {88 6731−13−54−82−90−78−46 −4 38 73 90 85 61 22− 22 −61−85−90−73−38 4 46 78 9082 54 13−31−67−88} {87 57 9−43−80−90−70−25 25 70 90 80 43 −9−57−87− 87−57 −9 43 80 90 70 25−25−70−90−80−43 9 57 87} {85 46−13−67−90−73−22 3882 88 54 −4−61−90−78 31 31 78 90 61 4−54−88−82−38 22 73 90 67 13−46−85}{83 36−36−83−83−36 36 83 83 36−36−83−83−36 36 83 83 36−36−83−83−36 36 8383 36−36−83−83−36 36 83} {82 22−54−90−61 13 78 85 31−46−90−67 4 73 8838− 38−88−73 −4 67 90 46−31−85−78−13 61 90 54−22−82} {80 9−70−87−25 5790 43−43−90−57 25 87 70 −9−80− 80 −9 70 87 25−57−90−43 43 90 57−25−87−709 80} {78 −4−82−73 13 85 67−22−88−61 31 90 54−38−90−46 90 38−54−90−31 6188 22−67−85−13 73 82 4−78} {75−18−89−50−50 89 18−75−75 18 89 50−50−89−1875 75−18−89−50 50 89 18−75−75 18 89 50−50−89−18 75} {73−31−90−22 7867−38−90−13 82 61−46−88 −4 85 54− 54−85 4 88 46−61−82 13 90 38−67−78 2290 31−73} {70−43−87 9 90 25−80−57 57 80−25−90−9 87 43−70−70 43 87−9−90−25 80 57−57−80 25 90 9−87−43 70} {67−54−78 38 85−22−90 4 9013−88−31 82 46−73−61 61 73−46−82 31 88−13−90 −4 90 22−85−38 78 54−67}{64−64−64 64 64−64−64 64 64−64−64 64 64−64−64 64 64−64−64 64 64−64−64 6464−64−64 64 64−64−64 64} {61−73−46 82 31−88−13 90 −4−90 22 85−38−78 5467− 67−54 78 38−85−22 90 4−90 13 88−31−82 46 73−61} {57−80−25 90 −9−8743 70−70−43 87 9−90 25 80−57−57 80 25−90 9 87−43−70 70 43−87 −9 90−25−8057} {54−85 −4 88−46−61 82 13−90 38 67−78−22 90−31−73 73 31−90 2278−67−38 90−13−82 61 46−88 4 85−54} {50−89 18 75−75−18 89−50−50 89−18−7575 18−89 50 50−89 18 75−75−18 89−50−50 89−18−75 75 18−89 50} {46−90 3854−90 31 61−88 22 67−85 13 73−82 4 78−78 −4 82−73−13 85−67−22 88−61 3190−54−38 90−46} {43−90 57 25−87 70 9−80 80 −9−70 87−25−57 90−43−4390−57−25 87−70 −9 80−80 9 70−87 25 57−90 43} {38−88 73 −4−67 90−46−3185−78 13 61−90 54 22−82 82− 22−54 90−61−13 78−85 31 46−90 67 4−73 88−38}{36−83 83−36−36 83−83 36 36−83 83−36−36 83−83 36 36−83 83−36−36 83−83 3636−83 83−36−36 83−83 36} {31−78 90−61 4 54−88 82−38−22 73−90 67−13−4685−85 46 13−67 90−73 22 38−82 88−54 −4 61−90 78−31} {25 −70 90−80 439−57 87−87 57 −9−43 80−90 70−25−25 70−90 80−43 −9 57−87 87−57 9 43−8090−70 25} {22 −61 85−90 73−38 −4 46−78 90−82 54−13−31 67−88 88−67 3113−54 82−90 78−46 4 38−73 90−85 61−22} {18−50 75−89 89−75 50−18−18 50−7589−89 75−50 18 18−50 75−89 89−75 50−18−18 50−75 89−89 75−50 18} {13−3861−78 88−90 85−73 54−31 4 22−46 67−82 90−90 82−67 46−22 −4 31−54 73−8590−88 78−61 38−13} {9−25 43−57 70−80 87−90 90−87 80−70 57−43 25 −9 −925−43 57−70 80−87 90−90 87−80 70−57 43−25 9} {4−13 22−31 38−46 54−6167−73 78−82 85−88 90−90 90−90 88−85 82−78 73−67 61−54 46−38 31−22 13 −4}

The DCT-2 cores show symmetry/anti-symmetry characteristics. Thus, aso-called “partial butterfly” implementation is supported to reduce thenumber of operation counts (e.g., multiplications, adds/subs, shifts),and identical results of matrix multiplication can be obtained usingpartial butterfly.

Two sub-block transforms can be provided, such as in VVC. A firstsub-block transform is SVT or SBT. For example, in JVET-J0024,JVET-K0139, and JVET-L0358, a spatially varying transform (SVT) schemeis proposed. With SVT, for inter prediction residuals, there may be onlya residual block in the coding block. Since the residual block issmaller than the coding block, the transform size in SVT is smaller thanthe coding block size. For the region which is not covered by theresidual block or transform, zero residual may be assumed.

SVT can also be called Sub-block Transform (SBT) such as in JVET-L0358.Examples of the sub-block types (e.g., SVT-H, SVT-V), sizes, andpositions (e.g., left half, left quarter, right half, right quarter, tophalf, top quarter, bottom half, bottom quarter) supported in SBT areshown in FIGS. 7A-7D. FIGS. 7A-7D illustrate the sub-block types (SVT-H,SVT-V), and the positions (left half, right half, top half, bottom half)supported in SBT respectively. The shaded region labeled by the letter“A” is a residual block with transform, and the other region is assumedto be a zero residual without transform.

A second sub-block transform is Intra Sub-Partitions (ISP). The ISPcoding mode divides luma intra-predicted blocks vertically orhorizontally into 2 or 4 sub-partitions depending on the block sizedimensions, as shown in Table 1. FIG. 8 and FIG. 9 show examples of thetwo possibilities. FIG. 8 illustrates an exemplary division of a 4×8block or an 8×4 block. FIG. 9 illustrates an exemplary division of ablock that is not one of a 4×8 block, an 8×4 block, or a 4×4 block. Allsub-partitions can fulfill the condition of having at least 16 samples.For chroma components, ISP is not applied.

TABLE 1 Number of sub-partitions depending on the block size Block SizeNumber of Sub-Partitions 4 × 4 Not divided 4 × 8 and 8 × 4 2 All othercases 4

In some embodiments, for each of these sub-partitions, a residual signalcan be generated by entropy decoding the coefficients sent by theencoder and then inverse quantizing and inverse transforming thecoefficients. Then, the sub-partition is intra predicted, and finally,the corresponding reconstructed samples are obtained by adding theresidual signal to the prediction signal. Therefore, the reconstructedvalues of each sub-partition can be available to generate the predictionof the next one, which can repeat the process and so on. Allsub-partitions can share the same intra mode.

In some embodiments, the ISP algorithm will only be tested with intramodes that are part of the MPM list. For this reason, if a block usesISP, then the MPM flag can be inferred to be one. If ISP is used for acertain block, then the MPM list can be modified to exclude the DC modeand to prioritize horizontal intra modes for the ISP horizontal splitand vertical intra modes for the vertical one.

In ISP, each sub-partition can be regarded as a sub-TU, since thetransform and reconstruction is performed individually for eachsub-partition.

Besides 4-point, 8-point, 16-point and 32-point DCT-2 transforms such asin HEVC, additional 2-point and 64-point DCT-2 can also be included asprimary transforms, such as in VVC. The 64-point DCT-2 core defined inVVC can be shown below as a 64×64 matrix:

   {   { aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa,  aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,  aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa }   { bf, bg, bh, bi, bj,bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca,  cb,cc, cd, ce, cf, cg, ch, ci, cj, ck, −ck, −cj, −ci, −ch, −cg, −cf, −ce,−cd, −cc, −ch, −ca, −bz, −by,  −bx, −bw, −bv, −bu, −bt, −bs, −br, −bq,−bp, −bo, −bn, −bm, −bl, −bk, −bj, −bi,  −bh, −bg, −bf }   { ap, aq, ar,as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, −be, −bd, −bc, −bb,−ba, −az,  −ay, −ax, −aw, −av, −au, −at, −as, −ar,  −aq, −ap, −ap, −aq,−ar, −as, −at, −au, −av, −aw, −ax, −av, −az, −ba, −bb, −bc, −bd, −be,be, bd, bc, bb,  ba, az, ay, ax, aw, av, au, at, as, ar, aq, ap }   {bg, bj, bm, bp, bs, bv, by, cb, ce, ch, ck, −ci, −cf, −cc, −bz, −bw,−bt, −bq, −bn, −bk, −bh, −bf,  −bi, −bl, −bo, −br, −bu, −bx, −ca, −cd, −cg, −cj, cj, cg, cd, ca, bx, bu, br, bo, bl, bi, bf, bh, bk, bn, bq,bt, bw, bz, cc, cf, ci,  −ck, −ch, −ce, −cb, −by, −bv, −bs, −bp, −bm,−bj, −bg }   { ah, ai, aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak,−aj, −ai, −ah, −ah, −ai, −aj, −ak, −al, −am,  −an, −ao, ao, an, am, al,ak, aj, ai, ah, ah, ai, aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak, −aj, −ai, −ah, −ah, −ai, −aj, −ak, −al, −am, −an, −ao, ao, an, am, al,ak, aj, ai, ah }   { bh, bm, br, bw, cb, cg, −ck, −cf, −ca, −bv, −bq,−bl, −bg, −bi, −bn, −bs, −bx, −cc, −ch, cj, ce, bz,  bu, bp, bk, bf, bj,bo, bt, by, cd, ci, −ci, −cd, −by, −bt, −bo, −bj, −bf, −bk, −bp, −bu,−bz, −ce, −cj,  ch, cc, bx, hs, bn, bi, bg, bl, bq, bv, ca, cf, ck, −cg,−cb, −bw,  −br, −bm, −bh }   { aq, at, aw, az, bc, −be, −bb, −ay, −av,−as, −ap, −ar, −au, −ax, −ba, −bd, bd, ba, ax, au, ar, ap,  as, av, ay,bb, be, −bc, −az, −aw,  −at, −aq, −aq, −at, −aw, −az, −bc, be, bb, ay,av, as, ap, ar, au, ax, ba, bd, −bd, −ba, −ax, −au,  −ar, −ap, −as, −av,−ay, −bb, −be, bc, az, aw, at, aq }   { bi, bp, bw, cd, ck, −ce, −bx,−bq, −bj, −bh, −bo, −bv, −cc, −cj, cf, by, br, bk, bg, bn, bu, cb,  ci,−cg, −bz, −bs, −bl, −bf, −bm, −bt, −ca, −ch, ch, ca, bt, bm, bf, bl, bs,bz, cg, −ci, −cb, −bu,  −bn, −bg, −bk, −br, −by, −cf, cj, cc, bv, bo,bh, bj, bq, bx, ce, −ck, −cd, −bw, −bp, −bi }   { ad, ae, af, ag, −ag,−af, −ae, −ad, −ad, −ae, −af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag,−af,  −ae, −ad, −ad, −ae, −af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag,−af, −ae, −ad, −ad, −ae, −af, −ag, ag,  af, ae, ad, ad, ae, af, ag, −ag,−af, −ae, −ad, −ad, −ae, −af, −ag, ag, af, ae, ad }   { bj, bs, cb, ck,−cc, −bt, −bk, −bi, −br, −ca, −cj, cd, bu, bl, bh, bq, bz, ci, −ce, −bv,−bm, −bg,  −bp, −by, −ch, cf, bw, bn, bf, bo, bx, cg, −cg, −bx, −bo,−bf, −bn, −bw, −cf, ch, by, bp, bg, bm,  bv, ce, −ci, −bz, −bq, −bh,−bl, −bu, −cd, cj, ca, br, bi, bk, bt, cc, −ck, −cb, −bs, −bj }   { ar,aw, bb, −bd, −ay, −at, −ap, −au, −az, −be, ba, av, aq, as, ax, bc, −bc,−ax, −as, −aq, −av, −ba,  be, az, au, ap, at, ay, bd, −bb, −aw, −ar,−ar, −aw, −bb, bd, ay, at, ap, au, az, be, −ba, −av,  −aq, −as, −ax,−bc, bc, ax, as, aq, av, ca, −be, −az, −au, −ap, −at, −ay, −bd, bb, aw,ar }   { bk, bv, cg, −ce, −bt, −bi, −bm, −bx, −ci, cc, br, bg, bo, bz,ck, −ca, −bp, −bf, −bq, −cb, cj, by,  bn, bh, bs, cd, −ch, −bw, −bl,−bj, −bu, −cf, cf', bu, bj, bl, bw, ch, −cd, −bs, −bh, −bn, −by, −cj, cb, bq, bf, bp, ca, −ck, −bz, −bo, −bg, −br, −cc, ci, bx, bm, bi, bt,ce, −cg, −bv, −bk }   { ai, al, ao, −am, −aj, −ah, −ak, −an, an, ak, ah,aj, am, −ao, −al, −ai, −ai, −al, −ao, am, aj, ah,  ak, an, −an, −ak,−ah, −aj, −am, ao, al, ai, ai, al, ao, −am, −aj, −ah, −ak, −an, an, ak,ah, aj, am,  −ao, −al, −ai, −ai, −al, −ao, am, aj, ah, ak, an, −an, −ak,−ah, −aj, −am, ao, al, ai }   { bl, by, −ck, −bx, −bk, −bm, −bz, cj, bw,bj, bn, ca, −ci, −bv, −bi, −bo, −cb, ch, bu, bh, bp, cc,  −cg, −bt, −bg,−bq, −cd, cf, bs, bf, br, ce, −ce, −br, −bf, −bs, −cf, cd, bq, bg, bt,cg, −cc, −bp, −bh,  −bu, −ch, cb, bo, bi, bv, ci, −ca, −bn, −bj, −bw,−cj, bz, bm, bk, bx, ck, −by, −bl }   { as, az, −bd, −aw, −ap, −av, −bc,ba, at, ar, ay, −be, −ax, −aq, −au, −bb, bb, au, aq, ax, be, −ay,  −ar,−at, −ba, bc, av, ap, aw, bd, −az, −as, −as, −az, bd, aw, ap, av, bc,−ba, −at, −ar, −ay, be,  ax, aq, au, bb, −bb, −au, −aq, −ax, −be, ay,ar, at, ba, −bc, −av, −ap, −aw, −bd, az, as }   { bm, cb, −cf, −bq, −bi,−bx, cj, bu, bf, bt, ci, −by, −bj, −bp, −ce, cc, bn, bl, ca, −cg, −br,−bh,  −bw, ck, bv, bg, bs, ch, −bz, −bk, −bo, −cd, cd, bo, bk, bz, −ch,−bs, −bg, −bv, −ck, bw, bh, br,  cg, −ca, −bl, −bn, −cc, ce, bp, bj, by,−ci, −bt, −bf, −bu, −cj, bx, bi, bq, cf, −cb, −bm }   { ab, ac, −ac,−ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac,−ab, −ab, −ac,  ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac,−ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab,  −ac, ac, ab, ab, ac, −ac,−ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab }   { bn, cc,−ca, −bj, −br, −ci, bw, bf, by, −cj, −bs, −bi, −bz, cf, bo, bm, cd, −cb,−bk, −bq, −ch, bx,  bg, bu, −ck, −bt, −bh, −by, cg, bp, bl, cc, −cc,−bl, −bp, −cg, by, bh, bt, ck, −bu, −bg, −bx, ch,  bq, bk, cb, −cd, −bm,−bo, −cf, bz, bi, bs, cj, −bv, −bf, −bw, ci, br, bj, ca, −ce, −bn }   {at, bc, −ay, −ap, −ax, bd, au, as, bb, −az, −aq, −aw, be, av, ar, ba,−ba, −ar, −av, −be, aw, aq,  az, −bb, −as, −au, −bd, ax, ap, ay, −bc,−at, −at, −bc, ay, ap, ax, −bd, −au, −as, −bb, az, aq, aw,  −be, −av,−ar, −ba, ba, ar, av, be, −aw, −aq, −az, bb, as, au, bd, −ax, −ap, −ay,be, at }   { bo, ch, −bv, −bh, −ca, cc, bj, bt, −cj, −bq, −bm, −cf, bx,bf, by, −ce, −bl, −br, −ck, bs, bk, cd,  −bz, −bg, −bw, cg, bn, bp, ci,−bu, −bi, −cb, cb, bi, bu, −ci, −bp, −bn, −cg, bw, bg, bz, −cd, −bk, −bs, ck, br, bl, ce, −by, −bf, −bx, cf, bm, bq, cj, −bt, −bj, −cc, ca,bh, bv, −ch, −bo }   { aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al,an, ai, ak, −ao, −aj, −aj, −ao, ak, ai, an, −al,  −ah, −am, am, ah, al,−an, −ai, −ak, ao, aj, aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al,an, ai,  ak, −ao, −aj, −aj, −ao, ak, ai, an, −al, −ah, −am, am, ah, al,−an, −ai, −ak, ao, aj }   { bp, ck, −bq, −ho, −cj, br, bn, ci, −bs, −bm,−ch, bt, bl, cg, −bu, −bk, −cf, bv, bj, ce, −bw, −bi,  −cd, bx, bh, cc,−by, −bg, −cb, bz, bf, ca, −ca, −bf, −bz, cb, bg, by, −cc, −bh, −bx, cd,bi, bw,  −ce, −bj, −bv, cf, bk, bu, −cg, −bl, −bt, ch, bm, bs, −ci, −bn,−br, cj, bo, bq, −ck, −bp }   { au, −be, −at, −av, bd, as, aw, −bc, −ar,−ax, bb, aq, ay, −ba, −ap, −az, az, ap, ba, −ay, −aq, −bb,  ax, ar, bc,−aw, −as, −bd, av, at, be, −au, −au, be, at, av, −bd, −as, −aw, bc, ar,ax, −bb, −aq, −ay,  ba, ap, az, −az, −ap, −ba, ay, aq, bb, −ax, −ar,−bc, aw, as, bd, −av, −at, −be, au }   { bq, −ci, −bl, −bv, cd, bg, ca,−by, −bi, −cf, bt, bn, ck, −bo, −bs, cg, bj, bx, −cb, −bf, −cc, bw,  bk,ch, −br, −bp, cj, bm, bu, −ce, −bh, −bz, bz, bh, ce, −bu, −bm, −cj, bp,br, −ch, −bk, −bw, cc,  bf, ch, −bx, −bj, −cg, bs, bo, −ck, −bn, −bt,cf, bi, by, −ca, −bg, −cd, bv, bl, ci, −bq }   { ae, −ag, −ad, −af, af,ad, ag, −ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af,ad,  ag, −ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af,ad, ag, −ae, −ae, ag, ad, af, −af,  −ad, −ag, ae, ae, −ag, −ad, −af, af,ad, ag, −ae, −ae, ag, ad, af, −af, −ad, −ag, ae }   { br, −cf, −bg, −cc,bu, bo, −ci, −bj, −bz, bx, bl, ck, −bm, −bw, ca, bi, ch, −bp, −bt, cd,bf, ce,  −bs, −bq, cg, bh, ch, −bv, −bn, cj, bk, by, −by, −bk, −cj, bn,bv, −cb, −bh, −cg, bq, bs, −ce, −bf,  −cd, bt, bp, −ch, −bi, −ca, bw,bm, −ck, −bl, −bx, bz, bj, ci, −bo, −bu, cc, bg, cf, −br }   { av, −bb,−ap, −bc, au, aw, −ba, −aq, −bd, at, ax, −az, −ar, −be, as, ay, −ay,−as, be, ar, az, −ax,  −at, bd, aq, ha, −aw, −au, bc, ap, bb, −av, −av,bb, ap, bc, −au, −aw, ba, aq, bd, −at, −ax, az,  ar, be, −as, −ay, ay,as, −be, −ar, −az, ax, at, −bd, −aq, −ba, aw, au, −bc, −ap, −bb, av }  { bs, −cc, −bi, −cj, bl, bz, −bv, −bp, cf, bf, cg, −bo, −bw, by, bm,−ci, −bh, −cd, br, bt, −cb, −bj,  −ck, bk, ca, −bu, −bq, ce, bg, ch,−bn, −bx, bx, bn, −ch, −bg, −ce, bq, bu, −ca, −bk, ck, bj, cb,  −bt,−br, cd, bh, ci, −bm, −by, bw, bo, −cg, −bf, −cf, bp, bv, −bz, −bl, cj,bi, cc, −bs }   { ak, −am, −ai, ao, ah, an, −aj, −al, al, aj, −an, −ah,−ao, ai, am, −ak, −ak, am, ai, −ao, −ah, −an,  aj, al, −al, −aj, an, ah,ao, −ai, −am, ak, ak, −am, −ai, ao, ah, an, −aj, −al, al, aj, −an, −ah,−ao,  ai, am, −ak, −ak, am, ai, −ao, −ah, −an, aj, al, −al, −aj, an, ah,ao, −ai, −am, ak }   { bt, −bz, −bn, cf, bh, ck, −bi, −ce, bo, by, −bu,−bs, ca, bm, −cg, −bg, −cj, bj, cd, −bp, −bx, by,  br, −cb, −bl, ch, bf,ci, −bk, −cc, bq, bw, −bw, −bq, cc, bk, −ci, −bf, −ch, bi, cb, −br, −by,bx, bp,  −cd, −bj, cj, bg, cg, −bm, −ca, bs, bu, −by, −bo, ce, bi, −ck,−bh, −cf, bn, bz, −bt }   { aw, −ay, −au, ba, as, −bc, −aq, be, ap, bd,−ar, −bb, at, az, −av, −ax, ax, av, −az, −at, bb, ar,  −bd, −ap, −be,aq, bc, −as, −ba, au, ay, −aw, −aw, ay, au, −ba, −as, bc, aq, −be, −ap,−bd, ar, bb,  −at, −az, av, ax, −ax, −av, az, at, −bb, −ar, bd, ap, be,−aq, −bc, as, ba −au, −ay, aw }   { bu, −bw, −bs, by, bq, −ca, −bo, cc,bm, −ce, −bk, cg, bi, −ci, −bg, ck, bf, cj, −bh, −ch, bj, cf,  −bl, −cd,bn, cb, −bp, −bz, br, bx, −bt, −bv, bv, bt, −bx, −br, bz, bp, −cb, −bn,cd, bl, −cf, −bj,  ch, bh, −cj, −bf, −ck, bg, ci, −bi, −cg, bk, ce, −bm,−cc, bo, ca, −bq, −by, bs, bw, −bu }    aa, −aa, −aa, aa, aa, −aa, −aa,aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa,  −aa,aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa. −aa,aa, aa, −aa, −aa, aa, aa,  −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa,aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa }   { bv, −bt, −bx, br, bz, −bp,−cb, bn, cd, −bl, −cf, bj, ch, −bh, −cj, bf, −ck, −bg, ci, bi, −cg, −bk, ce, bm, −cc, −bo, ca, bq, −by, −bs, bw, bu, −bu, −bw, bs, by, −bq, −ca,bo, cc, −bm, −ce, bk, cg,  −bi, −ci, bg, ck, −bf, cj, bh, −ch, −bj, cf,bl, −cd, −bn, cb, hp, −bz, −br, bx, bt, −bv }   { ax, −av, −az, at, bb,−ar, −bd, ap, −be, −aq, bc, as, −ba, −au, ay, aw, −aw, −ay, au, ba, −as,−bc,  aq, bc, −ap, bd, ar, −bb, −at, az, av, −ax, −ax, av, az, −at, −bb,ar, bd, −ap, be, aq, −bc, −as, ba,  au, −ay, −aw, aw, ay, −au, −ba, as,bc, −aq, −be, ap, −bd, −ar, bb, at, −az, −ay, ax }   { bw, −bq, −cc, bk,ci, −bf, ch, bt, −cb, −br, bv, bx, −bp, −cd, bj, cj, −bg, cg, bm, −ca,−bs, bu,  by, −bo, −ce, bi, ck, −bh, cf, bn, −bz, −bt, bt, bz, −bn, −cf,bh, −ck, −bi, ce, bo, −by, −bu, bs,  ca, −bm, −cg, bg, −cj, −bj, cd, bp,−bx, −bv, br, cb, −bl, −ch, bf, −ci, −bk, cc, bq, −bw }   { al, −aj,−an, ah, −ao, −ai, am, ak, −ak, −am, ai, ao, −ah, an, aj, −at, −al, aj,an, −ah, ao, ai,  −am, −ak, ak, am, −ai, −ao, ah, −an, −aj, al, al, −aj,−an, ah, −ao, −ai, am, ak, −ak, −am, ai, ao,  −ah, an, aj, −al, −al, aj,an, −ah, ao, ai, −am, −ak, ak, am, −ai, −ao, ah, −an, −aj, al }   { bx,−bn, −ch, bg, −ce, −bq, bu, ca, −bk, −ck, bj, −cb, −bt, br, cd, −bh, ci,bm, −by, −bw, bo,  cg, −bf, cf, bp, −bv, −bz, bl, cj, −bi, cc, bs, −bs,−cc, bi, −cj, −bl, bz, bv, −bp, −cf, bf, −cg, −bo,  bw, by, −bm, −ci,bh, −cd, −br, bt, cb, −bj, ck, bk, −ca, −bu, bq, cc, −bg, ch, bn, −bx }  { ay, −as, −be, ar, −az, −ax, at, bd, −aq, ba, aw, −au, −bc, ap, −bb,−av, av, bb, −ap, bc, au, −aw,  −ba, aq, −bd, −at, ax, az, −ar, be, as,−ay, −ay, as, be, −ar, az, ax, −at, −bd, aq, −ba, −aw, au, bc,  −ap, bb,av, −av, −bb, ap, −bc, −au, aw, ba, −aq, bd, at, −ax, −az, ar, −be, −as,ay }  −{ by, −bk, cj, bn, −bv, −cb, bh, −cg, −bq, bs, cc, −bf, cd, bt,−bp, −ch, bi, −ca, −bw, bm, ck, −bl,  bx, bz, −bj, ci, bo, −bu, −cc, bg,−cf, −br, br, cf, −bg, cc, bu, −bo, −ci, bj, −bz, −bx, bl, −ck,  −bm,bw, ca, −bi, ch, bp, −bt, −cd, bf, −ce, −bs, bq, cg, −bh, cb, bv, −bn,−cj, bk, −by }   { af, −ad, ag, ae, −ae, −ag, ad, −af, −af, ad, −ag,−ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag,  ad, −af, −af, ad, −ag,−ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag, ad, −af, −af, ad, −ag,−ae, ae,  ag, −ad, af, af, −ad, ag, ae, −ae, −ag, ad, −af, −af, ad, −ag,−ae, ae, ag, −ad, af }   { bz, −bh, ce, bu, −bm, cj, bp, −br, −ch, bk,−bw, −cc, bf, −cb, −bx, bj, −cg, −bs, bo, ck, −bn, bt,  cf, −bi, by, ca,−bg, cd, bv, −bl, ci, bq, −bq, −ci, bl, −bv, −cd, bg, −ca, −by, bi, −cf,−bt, bn, −ck,  −bo, bs, cg, −bj, bx, cb, −bf, cc, bw, −bk, ch, hr, −bp,−cj, bm, −bu, −ce, bh, −hz }  { az, −ap, ba, ay, −aq, bb, ax, −ar, bc,aw, −as, bd, av, −at, be, au, −au, −be, at, −ay, −bd, as,  −aw, −bc, ar,−ax, −bb, aq, −ay, −ba, ap, −az, −az, ap, −ba, −ay, aq, −bb, −ax, ar,−bc, −aw, as, −bd,  −ay, at, −be, −au, au, be, −at, av, bd, −as, aw, bc,−ar, ax, bb, −aq, ay, ba, −ap, az }   { ca, −bf, bz, cb, −bg, by, cc,−bh, bx, cd, −bi, bw, ce, −bj, bv, cf, −bk, bu, cg, −bl, bt, ch,  −bm,bs, ci, −bn, br, cj, −bo, bq, ck, −bp, bp, −ck, −bq, bo, −cj, −br, bn,−ci, −bs, bm, −ch, −bt, bl,  −cg, −bu, bk, −cf, −bv, bj, −ce, −bw, bi,−cd, −bx, bh, −cc, −by, bg, −cb, −bz, bf, −ca }   { am, −ah, al, an,−ai, ak, ao, −aj, aj, −ao, −ak, ai, −an, −al, ah, −am, −am, ah, −al,−an, ai, −ak,  −ao, aj, −aj, ao, ak, −ai, an, al, −ah, am, am, −ah, al,an, −ai, ak, ao, −aj, aj, −ao, −ak, ai, −an,  −al, ah, −am, −am, ah,−al, −an, ai, −ak, −ao, aj, −aj, ao, ak, −ai, an, al, −ah, am }   { cb,−bi, bu, ci, −bp, bn, −cg, −bw, bg, −bz, −cd, bk, −bs, −ck, br, −bl, ce,by, −bf, bx, cf, −bm,  bq, −cj, −bt, bj, −cc, −ca, bh, −bv, −ch, bo,−bo, ch, bv, −bh, ca, cc, −bj, bt, cj, −bq, bm, −cf  −bx, bf, −by, −ce,bl, −br, ck, bs, −bk, cd, bz, −bg, bw, cg, −bn, bp, −ci, −bu, bi, −cb }  { ba, −ar, av, −be, −aw, aq, −az, −bb, as, −au, bd, ax, −ap, ay, bc,−at, at, −bc, −ay, ap, −ax, −bd,  au, −as, bb, az, −ay, aw, be, −av, ar,−ba, −ba, ar, −av, be, aw, −ay, az, bb, −as, au, −bd, −ax,  ap, −ay,−bc, at, −at, bc, ay, −ap, ax, bd, −au, as, −bb, −az, aq, −aw, −be, av,−ar, ba }   { cc, −bl, bp, −cg, −by, bh, −bt, ck, bu, −bg, bx, ch, −bq,bk, −cb, −cd, bm, −bo, cf, bz, −bi, bs,  −cj, −bv, bf, −bw, −ci, br,−bj, ca, ce, −bn, bn, −ce, −ca, bj, −br, ci, bw, −bf, bv, cj, −bs, bi,−bz,  −cf, bo, −bm, cd, ch, −bk, bq, −ch, −bx, bg, −hu, −ck, bt, −bh,by, cg, −bp, bl, −cc }   { ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab,ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab,  −ab, ac, ac, −ab,ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab,ab, −ac,  −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab,ab, −ac, −ac, ab, −ab, ac }   { cd, −bo, bk, −bz, −ch, bs, −bg, bv, −ck,−bw, bh, −br, cg, ca, −bl, bn, −cc, −ce, bp, −bj, by, ci,  −bt, bf, −bu,cj, bx, −bi, bq, −cf, −cb, bm, −bm, ch, cf, −bq, bi, −bx, −cj, bu, −bf,bt, −ci, −by,  bj, −bp, ce, cc, −bn, bl, −ca, −cg, br, −bh, bw, ck, −bv,bg, −bs, ch, bz, −bk, bo, −cd }   { bb, −au, aq, −ax, be, ay, −ar, at,−ba, −bc, av, −ap, aw, −bd, −az, as, −as, az, bd, −aw, ap, −av,  bc, ba,−at, ar, −ay, −be, ax, −aq, au, −bb, −bb, au, −aq, ax, −be, −ay, ar,−at, ba, bc, −av, ap,  −aw, bd, az, −as, as, −az, −bd, aw, −ap, av, −bc,−ba, at, −ar, ay, be, −ax, aq, −au, bb }   { ce, −br, bf, −bs, cf, cd,−bq, bg, −bt, cg, cc, −bp, bh, −bu, ch, cb, −bo, bi, −bv, ci, ca, −bn, bj, −bw, cj, bz, −bm, bk, −bx, ck, by, −bl, bl, −by, −ck, bx, −bk, bm,−bz, −cj, bw, −bj, bn, −ca,  −ci, bv, −bi, bo, −cb, −ch, bu, −bh, bp,−cc, −cg, bt, −bg, bq, −cd, −cf, bs, −bf, br, −cc }    an, −ak, ah, −aj,am, ao, −al, ai, −ai, al, −ao, −am, aj, −ah, ak, −an, −an, ak, −ah, aj,−am, −ao,  al, −ai, ai, −al, ao, am, −aj, ah, −ak, an, an, −ak, ah, −aj,am, ao, −al, ai, −ai, al, −ao, −am, aj,  −ah, ak, −an, −an, ak, −ah, aj,−am, −ao, al, −ai, ai, −al, ao, am, −aj, ah, −ak, an }   { cf, −bu, bj,−bl, bw, −ch, −cd, bs, −bh, bn, −by, cj, cb, −bq, bf, −bp, ca, ck, −bz,bo, −bg, br,  −cc, −ci, bx, −bm, bi, −bt, ce, cg, −bv, bk, −bk, bv, −cg,−ce, bt, −bi, bm, −bx, ci, cc, −br, bg,  −bo, bz, −ck, −ca, bp, −bf, bq,−cb, −cj, by, −bn, bh, −bs, cd, ch, −bw, bl, −bj, bu, −cf }   { bc, −ax,as, −aq, av, −ba, −be, az, −au, ap, −at, ay, −bd, −bb, aw, −ar, ar, −aw,bb, bd, −ay, at,  −ap, an, −az, be, ba, −av, aq, −as, ax, −bc, −bc, ax,−as, aq, −av, ba, be, −az, au, −ap, at, −ay,  bd, bb, −aw, ar, −ar, aw,−bb, −bd, ay, −at, ap, −au, az, −be, −ba, av, −aq, as, −ax, bc }   { cg,−bx, bo, −bf, bn, −bw, cf, ch, −by, bp, −bg, bm, −bv, ce, ci, −hz, bq,−bh, bl, −bu, cd, cj,  −ca, br, −bi, bk, −bt, cc, ck, −cb, bs, −bj, bj,−bs, cb, −ck, −cc, bt, −bk, bi, −br, ca, −cj, −cd, bu,  −bl, bh, −bq,bz, −ci, −ce, bv, −bm, bg, −bp, by, −ch, −cf, bw, −bn, bf, −bo, bx, −cg}   { ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae,−af, ag, ag, −af, ae, −ad, ad, −ae,  af, −ag, −ag, af, −ae, ad, −ad, ae,−af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad,  ae,−af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae,−af, ag }   { ch, −ca, bt, −bm, bf, −bl, bs, −bz, cg, ci, −cb, bu, −bn,bg, −bk, br, −by, cf, cj, −cc, bv, −bo,  bh, −bj, bq, −bx, ce, ck, −cd,bw, −bp, bi, −bi, bp, −bw, cd, −ck, −cc, bx, −bq, bj, −bh, bo, −bv,  cc,−cj, −cf, by, −br, bk, −bg, bn, −bu, cb, −ci, −cg, bz, −bs, bl, −bf, bm,−bt, ca, −ch }   { bd, −ba, ax, −au, ar, −ap, as, −av, ay, −bb, be, bc,−az, aw, −at, aq, −aq, at, −aw, az, −bc, −be,  bb, −ay, av, −as, ap,−ar, au, −ax, ha, −bd, −bd, ba, −ax, au, −ar, ap, −as, av, −ay, bb, −be,−bc,  az, −aw, at, −aq, aq, −at, aw, −az, bc, be, −bb, ay, −av, as, −ap,ar, −au, ax, −ba, bd }   { ci, −cd, by, −bt, bo, −bj, bf, −bk, bp, −bu,bz, −ce, cj, ch, −cc, bx, −bs, bn, −bi, bg, −bl, bq,  −bv, ca, −cf, ck,cg, −cb, bw, −br, bm, −bh, bh, −bm, br, −bw, cb, −cg, −ck, cf, −ca, bv,−bq, bl,  −bg, bi, −bn, bs, −bx, cc, −ch, −cj, ce, −bz, bu, −bp, bk,−bf, bj, −bo, bt, −by, cd, −ci }   { ao, −an, am, −al, ak, −aj, ai, −ah,ah, −ai, aj, −ak, al, −am, an, −ao, −ao, an, −am, al, −ak, aj,  −ai, ah,−ah, ai, −aj, ak, −al, am, −an, ao, ao, −an, am, −al, ak, −aj, ai, −ah,ah, −ai, aj, −ak, al,  −am, an, −ao, −ao, an, −am, al, −ak, aj, −ai, ah,−ah, ai, −aj, ak, −al, am, −an, ao }   { cj, −cg, cd, −ca, bx, −bu, br,−bo, bl, −bi, bf, −bh, bk, −bn, bq, −bt, bw, −bz, cc, −cf, ci, ck,  −ch,ce, −cb, by, −bv, bs, −bp, bm, −bj, bg, −bg, bj, −bm, bp, −bs, bv, −by,cb, −ce, ch, −ck, −ci,  cf, −cc, bz, −bw, bt, −bq, bn, −bk, bh, −bf, bi,−bl, bo, −br, bu, −bx, ca, −cd, cg, −cj }   { be, −bd, bc, −bb, ba, −az,ay, −ax, aw, −av, au, −at, as, −ar, aq, −ap, ap, −aq, ar, −as, at, −au, av, −aw, ax, −ay, az, −ba, bb, −bc, bd, −be, −be, bd, −bc, bb, −ha, az,−ay, ax, −aw, av, −au, at,  −as, ar, −aq, ap, −ap, aq, −ar, as, −at, au,−av, am, −ax, ay, −az, ba, −bb, bc, −bd, be }   { ck, −cj, ci, −ch, cg,−cf, ce, −cd, cc, −cb, ca, −bz, by, −bx, bw, −bv, bu, −bt, bs, −br, bq,−bp,  bo, −bn, bm, −bl, bk, −bj, bi, −bh, bg, −bf, bf, −bg, bh, −bi, bj,−bk, bl, −bm, bn, −bo, bp, −bq,  br, −bs, bt, −bu, bv, −bw, bx, −by, bz,−ca, cb, −cc, cd, −ce, cf, −cg, ch, −ci, cj, −ck }  }where{aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar,as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj,bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, by, bw, bx, by, bz, ca, cb,cc, cd, ce, cf, cg, ch, ci, cj, ck}={64, 83, 36, 89, 75, 50, 18, 90, 87,80, 70, 57, 43, 25, 9, 90, 90, 88, 85, 82, 78, 73, 67, 61, 54, 46, 38,31, 22, 13, 4, 91, 90, 90, 90, 88, 87, 86, 84, 83, 81, 79, 77, 73, 71,69, 65, 62, 59, 56, 52, 48, 44, 41, 37, 33, 28, 24, 20, 15, 11, 7, 2}

In addition to DCT-2 and 4×4 DST-7 which have been employed in HEVC, anAdaptive Multiple Transform (AMT, or also known as Enhanced MultipleTransform (EMT) or Multiple Transform Selection (MTS)) scheme has beenused in VVC for residual coding for both inter and intra coded blocks.The MTS uses multiple selected transforms from the DCT/DST familiesother than the current transforms in HEVC. The newly introducedtransform matrices are DST-7, DCT-8. Table 2 shows the basis functionsof the selected DST/DCT.

TABLE 2 Transform basis functions of DCT-2, DST-7 and DCT-8 for N-pointinput Transform Type Basis function T_(i)(j), i, j = 0, 1, . . . , N − 1DCT-2${T_{i}(j)} = {\omega_{0} \cdot \sqrt{\frac{2}{N}} \cdot {\cos \left( \frac{\pi \cdot i \cdot \left( {{2j} + 1} \right)}{2N} \right)}}$${{where}\mspace{14mu} \omega_{0}} = \left\{ \begin{matrix}\sqrt{\frac{2}{N}} & {i = 0} \\1 & {i \neq 0}\end{matrix} \right.$ DCT-8${T_{i}(j)} = {\sqrt{\frac{4}{{2N} + 1}} \cdot {\cos \left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {{2j} + 1} \right)}{{4N} + 2} \right)}}$DST-7${T_{i}(j)} = {\sqrt{\frac{4}{{2N} + 1}} \cdot {\sin \left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {j + 1} \right)}{{2N} + 1} \right)}}$

All the primary transform matrices, such as in VVC, may be used with8-bit representation. The AMT applies to the CUs with both width andheight smaller than or equal to 32, and whether applying AMT or not iscontrolled by a flag called mts_flag. When the mts_flag is equal to 0,only DCT-2 may be applied for coding the residue. When the mts_flag isequal to 1, an index mts_idx is further signalled using 2 bins tospecify the horizontal and vertical transform to be used according toTable 3, where value 1 means using DST-7 and value 2 means using DCT-8.

TABLE 3 Specification of trTypeHor and trTypeVer depending on mts_idx[ x][ y ][ cIdx ] mts_idx[ xTbY ][ yTbY ][ cIdx ] trTypeHor trTypeVer −1 00 0 1 1 1 2 1 2 1 2 3 2 2

An implicit MTS, such as in VVC Draft 4, may also be applied in casethat the above signaling based MTS (i.e., explicit MTS) is not used.With implicit MTS, the transform selection is made according to theblock width and height instead of signaling. More specifically, withimplicit MTS for example as proposed in JVET-M0303, DST-7 is selectedfor the shorter side of the block and DCT-2 is selected for the longerside of the block. The transform core, which is a matrix composed by thebasis vectors, of DST-7 can be represented below:

  4-point DST-7:  { a, b, c, d }  { c, c, 0, −c }  { d, −a, −c, b }  {b, −d, c, −a } where {a, b, c, d} = { 29, 55, 74, 84}. 8-point DST-7:  { a, b, c, d, e, f, g, h,}  { c, f, h, e, b, −a, −d, −g,}  { e, g, b,−c, −h, −d, a, f,}  { g, c, −d, −f, a, h, b, −e,}  { h, −a, −g, b, f,−c, −e, d,}  { f, −e, −a, g, −d, −b, h, −c,}  { d, −h, e, −a, −c, g, −f,b,}  { b, −d, f, −h, g, −e, c, −a,} where {a, b, c, d, e, f, g, h} ={17, 32, 46, 60, 71, 78, 85, 86}. l6-point DST-7:  { a, b, c, d, e, f,g, h, i, j, k, l, m, n, o, p,}  { c, f, i, l, o, o, l, i, f, c, 0, −c,−f, −i, −l, −o,}  { e, j, o, m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i,n,}  { g, n, l, e, −b, −i, −p, −j, −c, d, k, o, h, a, −f, −m,}  { i, o,f, −c, −l, −l, −c, f, o, i, 0, −i, −o, −f, c, l,}  { k, k, 0, −k, −k, 0,k, k, 0, −k, −k, 0, k, k, 0, −k,}  { m, g, −f, −n, −a, l, h, −e, −o, −b,k, i, −d, −p, −c, j,}  { o, c, −l, −f, i, l, −f, −l, c, o, 0, −o, −c, l,f, −i,}  { p, −a, −o, b, n, −c, −m, d, l, −e, −k, f, j, −g, −i, h,}  {n, −e, −i, j, d, −o, a, m, −f, −h, k, c, −p, b, l, −g,}  { l, −i, −c, o,−f, −f, o, −c, −i, l, o, −l, i, c, −0, f,}  { j, −m, c, g, −p, f, d, −n,i, a, −k, l, −b, −h, o, −e,}  { h, −p, i, −a, −g, o, −j, b, f, −n, k,−c, −e, in, −l, d,}  { f, −l, o, −i, c, c, −i, o, −i, f, 0, −f, l, −o,i, −c,}  { d, −h, l, −p, m, −i, e, −a, −c, g, −k, o, −n, j, −f, b,}  {b, −d, f, −h, j, −l, n, −p, o, −m, k, −i, g, −e, c, −a,} where {a, b, c,d, e, f, g, h, i, j, k, l, m, n, o, p} = { 9, 17, 25, 33, 41, 49, 56,62, 66, 72, 77, 81, 83, 87, 89, 90}. 32-point DST-7:  { a, b, c, d, e,f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C,D, E, F,}  { c, f, i, l, o, r, u, x, A, D, F, C, z, w, t, q, n, k, h, e,b, −a, −d, −g, −j, −m, −p, −s, −v, −y, −B, −E,}  { e, j, o, t, y, D, D,y, t, o, j, e, 0, −e, −j, −o, −t, −y, −D, −D, −y, −t, −o, −j, −e, 0, c,j, o, t, y, D,}  { g, n, u, B, D, w, p, i, b, −e, −l, −s, −z, −F, −y,−r, −k, −d, c, j, q, x, E, A, t, m, f, −a, −h, −o, −v, −C,}  { i, r, A,C, t, k, b, −g, −p, −y, −E, −v, −m, −d, e, n, w, F, x, o, f, −c, −l, −u,−D, −z, −q, −h, a, j, s, B,}  { k, v, F, u, j, −a, −l, −w, −E, −t, −i,b, m, x, D, s, h, −c, −n, −y, −C, −r, −g, d, o, z, B, q, f, −e, −p, −A,} { m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0,m, z, z, m, 0, −m, −z, −z, −m, 0, m, z,}  { o, D, t, e, −j, −y, −y, −j,e, t, D, o, 0, −o, −D, t, −e, j, y, y, j, −e, −t, −D, −o, 0, o, D, t, e,−j, −y,}  { q, E, n, −c, −t, −B, −k, f, w, y, h, −i, −z, −v, −e, l, C,s, b, −o, −F, −p, a, r, D, m, −d, −u, −A, −j, g, x,}  { s, A, h, −k, −D,−p, c, v, x, e, −n, −F, −m, f, y, u, b, −q, −C, −j, i, B, r, −a, −t, −z,−g, l, E, o, −d, −w,}  { u, w, b, −s, −y, −d, q, A, f, −o, −C, −h, m, E,j, −k, −F, −l, i, D, n, −g, −B, −p, e, z, r, −c, −x, −t, a, v,}  { w, s,−d, −A, −o, h, E, k, −l, −D, −g, p, z, c, −t, −v, a, x, r, −e, −B, −n,i, F, j, −m, −C, −f, q, y, b, −u,}  { y, o, −j, −D, −e, t, t, −e, −D,−j, o, y, 0, −y, −o, j, D, e, −t, −t, e, D, j, −o, −y, 0, y, o, −j, −D,−e,t,}  { A, k, −p, −v, e, E, f, −u, −q, j, B, a, −z, −l, o, w, −d, −E,−g, t, r, −i, −C, −b, y, m, −n, −x, c, D, h, −s,}  { C, g, −v, −a, o, u,−h, −B, a, D, f, −w, −m, p, t, −i, −A, b, E, e, −x, −l, q, s, −j, −z, c,F, d, −y, −k, r,}  { E, c, −B, −f, y, i, −v, −l, s, o, −p, −r, m, u, −j,−x, g, A, −d, −D, a, F, b, −C, −e, z, h, −w, −k, l, n, −q,}  { F, −a,−E, b, D, −c, −C, d, B, −e, −A, f, Z, −g, −y, h, x, −i, −w, j, v, −k,−u, l, t, −m, −s, n, r, −o, −q, p,}  { D, −e, −y, j, t, −o, −o, t, j,−y, −e, D, 0, −D, e, y, −j, −t, o, o, −t, −j, y, e, −D, 0, D, −e, −y, j,t, −o,}  { B, −i, −s, r, j, −A, −a, C, −h, −t, q, k, −z, −b, D, −g, −u,p, l, −y, −c, E, −f, −v, o, m, −x, −d, E, −e, −w, n,}  { z, −m, −m, z,0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m, −m, z, 0,−z, m, m, −z, 0, z, −m,}  { x, −q, −g, E, −j, −n, A, −c, −u, t, d, −B,m, k, −D, f, r, −w, −a, y, −p, −h, F, −i, −o, z, −b, −v, s, e, −C, l,} { v, −u, −a, w, −t, −b, x, −s, −c, y, −r, −d, z, −q, −e, A, −p, −f, B,−o, −g, C, −n, −h, D, −m, −i, E, −l, −j, F, −k,}  { t, −y, e, o, −D, j,j, −D, o, e, −y, t, 0, −t, y, −e, −o, D, −j, −j, D, −o, −e, y, −t, 0, t,−y, e, o, −D, j,}  { r, −C, k, g, −y, v, −d, −n, F, −o, −c, u, −z, h, j,−B, s, −a, −q, D, −l, −f, x, −w, e, m, −E, p, b, −t, A, −i,}  { p, −F,q, −a, −o, E, −r, b, n, −D, s, −c, −m, C, −t, d, l, −B, u, −e, −k, A,−v, f, j, −z, w, −g, −i, y, −x, h,}  { n, −B, w, −l, −e, s, −F, r, −d,−j, x, −A, m, a, −o, C, −v, h, f, t, E, −q, c, k, −y, z, −l, −b, p, −D,u, −g,}  { l, −x, C, −q, c, g, −s, E, −v, j, b, −n, z, −A, o, −c, −i, u,−F, t, −h, −d, p, −B, y, −m, a, k, −w, D, −r, f,}  { j, −t, D, −y, o,−e, −e, o, −y, D, −t, j, 0, −j, t, −D, y, −o, e, e, −o, y, −D, t, −j, 0,j, −t, D, −y, o, −e,}  { h, −p. x, −F, y, −q, i, −a, −g, o, −w, E, −z,r, −j, b, f, −n, v, −D, A, −s, k, −c, −e, m, −u, C, −B, t, −l, d,}  { f,−l, r, −x, D, −C, w, −q, k, −e, −a, g, −m, s, −y, E, −B, v, −p, j, −d,−b, h, −n, t, −z, F, −A, U, −o, i, −c,}  { d, −h, l, −p, t, −x, B, −F,C. −y, u, −q, m, −i, e, −a, −c, g, −k, o, −s, w, −A, E, −D, z, −v, r,−n, j, −f, b,}  { b, −d, f, −h, j, −l, n, −p, r, −t, v, −x, z, −B, D,−F, E, −C, A, −y, w, −u, s, −q, o, −m, k, −i, g, −e, c, −a,} where {a,b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y,z, A, B, C, D, E, F } = { 4, 9, 13, 17, 21, 26, 30, 34, 38, 42, 45, 50,53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 88, 88, 89,90, 90 }. 4-point DCT-8:  { a, b, c, d,}  { b, 0, −b, −b,}  { c, −b, −d,a,}  { d, −b, a, −c,} where {a, b, c, d} = { 84, 74, 55, 29}. 8-pointDCT-8:  { a, b, c, d, e, f, g, h,}  { b, e, h, −g, −d, −a, −c, −f,}  {c, h, −e, −a, −f, g, b, d}  { d, −g, −a, −h, c, e, −f, −b,}  { e, −d,−f, c, g, −b, −h, a,}  { f, −a, g, e, −b, h, d, −c,}  { g, −c, b, −f,−h, d, −a, e,}  { h, −f, d, −b, a, −c, e, −g,} where {a, b, c, d, e, f,g, h} = { 86, 85, 78, 71, 60, 46, 32, 17}. l6-point DCT-8:  { a, b, c,d, e, f, g, h, i, j, k, l, m, n, o, p,}  { b, e, h, k, n, 0, −n, −k, −h,−e, −b, −b, −e, −h, −k, −n,}  { c, h, m, −p, −k, −f, −a, −e, −j, −o, n,i, d, b, g, l,}  { d, k, −p, −i, −b, −f, −m, a, g, a, h, o, −l, −e, −c,−j,}  { e, n, −k, −b, −h, 0, h, b, k, −n, −e, −e, −n, k, b, h,}  { f, 0,−f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0, −f, −f,}  { g, −a, −a, −m, h, f,−o, −b, −l, i, e, −p, −c, −k, j, d,}  { h, −k, −e, n, b, 0, −b, −n, e,k, −h, −h, k, e, −n, −b,}  { i, −h, −j, g, k, −f, −l, e, m, −d, −n, c,o, −b, −p, a,}  { j, −e, −o, a, −n, −f, i, k, −d, −p, b, −m, −g, h, l,−c,}  { k, −b, n, h, −e, 0, e, −h, −n, b, −k, −k, b, −n, −h, e,}  { l,−b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −a, d, −g,}  { m, −e, d, −l,−n, f, −c, k, o, −g, b, −j, −p, h, −a, i,}  { n, −h, b, −e, k, 0, −k, e,−b, h, −n, −n, h, −b, e, −k,}  { o, −k, g, −c, b, −f, j, −n, −p, l, −h,d, −a, e, −i, m,}  { p, −n, l, −j, h, −f, d, −b, a, −c, e, −g, i, −k, m,−o,} where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p} = {90, 89,87, 83, 81, 77, 72, 66, 62, 56, 49, 41, 33, 25, 17, 9}. 32-point DCT-8: { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w,x, y, z, A, B, C, D, E, F,}  { b, e, h, k, n, q, t, w, z, C, F, −E, −B,−y, −v, −s, −p, −m, −j, −g, −d, −a, −c, −f, −i, −l, −o, −r, −u, −x, −A,−D,}  { c, h, m, r, w, B, 0, −B, −w, −r, −m, h, −c, −c, −h, −m, −r, −w,−B, 0, B, w, r, m, h, c, c, h, m, r, w, B,}  { d, k, r, y, F, −A, −t,−m, −f, −b, −i, −p, −w, −D, C, v, o, h, a, g, n, u, B −E, −x, −q, −j,−c, −e, −l, −s, −z,}  { e, n, w, F, −y, −p, −g, −c, −l, −u, −D, A, r, i,a, j, s, B, −C, −t, −k, −b, −h, −q, −z, E, v, m, d, f, o, x,}  { f, q,B, −A, −p, −e, −g, −r, −C, o, d, h, s, −y, −n, −c, −i, −t, −E, x, m, b,j, u, F, −w, −l, −a, −k, −v,}  { g, t, 0, −t, −g, −g, −t, 0, t, g, g, t,0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t,}  {h, w, −B, −m, −c, −r, 0 r, c, m, B, −w, −h, −h, −w, B, m, c, r, 0, −r,−c, −m, −B, w, h, h, w, −B, −m, −c, −r,}  { i, z, −w, −f, −l, −C, t, c,o, F, −q, −a, −r, E, n, d, u, −B, −k, −g, −x, y, h, j, A, −v, −e, −m,−D, s, b, p,}  { j, C, −r, −b, −u, z, g, m, F, −o, −e, −x, w, d, p, −E,−l, −h, −A, t, a, s, −B, −i, −k, −D, q, c, v, −y, −f, −n,}  { k, F, −m,−i, −D, o, g, B, −q, −e, −z, s, c, x, −u, −a, −v, w, b, t, −y, −d, −r,A, f, p, −C, −h, −n, E, j, l,}  { l, −E, −h, −p, A, d, t, −w, −a, −x, s,e, B, −o, −i, −F, k, m, −D, −g, −q, z, c, u, −v, −b, −y, r, f, C, −n,−j,}  { m, −B, −c, −w, r, h, 0, −h, −r, w, c, B, −m, −m, B, c, w, −r,−h, 0, h, r, −w, −c, −B, m, m, −B, −c, −w, r, h,}  { n, −y, −c, −D, i,s, −t, −h, E, d, x, −o, −m, z, b, C, −j, −r, u, g, −F, −e, −w, p, l, −A,−a, −B, k, q, −v, −f,}  { o, −v, −h, C, a, D, −g, −w, n, p, −u, −i, B,b, E, −f, −x, m, q, −t, −j, A, c, F, −e, −y, l, r, −s, −k, z, d,}  { p,−s, −m, v, j, −y, −g, B, d, −E, −a, −F, c, C, −f, −z, l, w, −l, −t, o,q, −r, −n, u, k, −x, −h, A, e, −D, −b,}  { q, −p, −r, o, s, −n, −t, m,u, −l, −v, k, w, −j, −x, i, y, −h, −z, g, A, −f, −B, e, C, −d, −D, c, E,−b, −F, a,}  { r, −m, −w, h, B, −c, 0, c, −B, −h, w, m, −r, −r, m, w,−h, −B, c, 0, −c, B, h, −w, −m, r, r, −m, −w, h, B, −c,}  { s, −j, −B,a, −C, −i, t, r, −k, −A, b, −D, −h, u, q, −l, −z, c, −E, −g, v, p, −m,−y, d, −F, −f, w, o, −n, −x, e,}  { t, −g, 0, g, −t, −t, g, 0, −g, t, t,−g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g,}  { u, −d, B, n, −k, −E, g, −r, −x, a, −y, −q, h, −F, −j, o, A, −c,v, t, −e, C, m, −l −D, f, −s, −w, b, −z, −p, i,}  { v, −a, w, u, −b, x,t, −c, y, s, −d, z, r, −e, A, q, −f, B, p, −g, C, o, −h, D, n, −i, E, m,−j, F, l, −k,}  { w, −c, r, B, −h, m, 0, −m , h, −B, −r, c, −w, −w, c,−r, −B, h, −m, 0, −h, B, r, −c, w, w, −c, r, B, −h, m,}  { x, −f, m, −E,−q, b, −t, −B, j, −i, A, u, −c, p, F, −n, e, −w, −y, g, −l, D, r, −a, s,C, k, h, −z, −v, d, −o,}  { y, −i, h, −x, −z, j, −g, A, −k, f, −v, −B,l, −e, u, C, −m, d, −t, −D, n, −c, s, E, −o, b, −r, −F, p, −a, q,}  { z,−l, c, −q, E, u, −g, l, −v, −D, p, −b, m, −A, −y, −k, −d, r, −F, −t, f,−i, w, C, −o, a, −n, B, x, −j, e, −s,}  { A, −o, c, −j, v, F, −t, h, −e,q, −C, −y, m, −a, l, −x, r, −f, g, −s, E, w, −k, b, −n, z, B, −p, d, −i,u,}  { B, −r, h, −c, m, −w, 0, w, −m, c, −h, r, −B, −B, r, −h, c, −m, w,0, −w, m, −c, h, −r, B, , −r, h, −c, m, −w,}  { C, −u, m, −e, d, −l, t,−B, −D, v, −n, f, −c, k, −s, A, E, −w, o, −g, b, −j, r, −z, −F, x, −p,h, −a, i, −q, y,}  { D, −x, r, −l, f, −a, g, −m, s, −y, E, C, −w, q, −k,e, −b, −n, t, −z, F, B, −v, p, −j, d, −c, i, −o, u, −A,}  { E, −A, w,−s, o, −k, g, −c, b, −f, j, −n, r, −v, z, −D, −F, B, −x, t, −p, l, −h,d, −a, e, −i, m, −q, u, −y, C,}  { F, −D, B, −z, x, −v, t, −r, p, −n, l,−j, h, −f, d, −b, a, −c, e, −g, i, −k, m, −o, q, −s, u, −w, y, −A, C,−E,} where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t,u, v, w, x, y, z, A, B, C, D, E, F } = {90, 90, 89, 88, 88, 86, 85, 84,82, 80, 78, 77, 74, 72, 68, 66, 63, 60, 56, 53, 50, 45, 42, 38, 34, 30,26, 21, 17, 13, 9, 4}.

In some examples, such as in VVC, when both the height and width of thecoding block is smaller than or equal to 64, the transform size canalways the same as the coding block size. When either the height orwidth of the coding block is larger than 64, when performing thetransform or intra prediction, the coding block can be further splitinto multiple sub-blocks, where the width and height of each sub-blockis smaller than or equal to 64, and one transform is performed on eachsub-block.

MTS can be enabled or disabled in SPS, such as in VVC Draft v5, with thefollowing syntaxes in Table 4.

TABLE 4 Syntax for enabling MTS in SPS seq_parameter_set_rbsp( ) {Descriptor ......  sps_mts_enabled_flag u(1)  if( sps_mts_enabled_flag ){   sps_explicit_mts_intra_enabled_flag u(1)  sps_explicit_mts_inter_enabled_flag u(1)  } ......

In addition, syntaxes elements for controlling implicit MTS, explicitMTS for intra coding and explicit MTS for inter coding can be describedin Table 5.

TABLE 5 Syntax elements for enabling implicit MTS, explicit MTS forintra and explicit MTS Implicit Explicit Explicit MTS MTS intra MTSinter sps_mts_enabled_flag 1 1 1 sps_explicit_mts_intra_enabled_flag 0 10/1 sps_explicit_mts_inter_enabled_flag 0/1 0/1 1

For some cases, DST-7 and/or DCT-8 can be used without being explicitlysignaled, such as in VVC Draft v5. For example, DST-7 and/or DCT-8 canbe used implicitly based on information that is available for both anencoder and a decoder. Exemplary cases include:

-   -   (a) ISP: For ISP mode, the horizontal transform is selected as        DST-7 as long as the block width is greater than or equal to 4        and less than or equal to 16, and the vertical transform is        selected as DST-7 as long as the block height is greater than or        equal to 4 and less than or equal to 16.    -   (b) SBT: For SBT mode, for a sub-TU located at the left half (or        quarter) or right half (or quarter) of current CU, the        horizontal transform is DCT-8 and DST-7, respectively.        Otherwise, when sub-TU has a same width as the current CU, DCT-2        is used. For a sub-TU located at the top half (or quarter) or        bottom half (or quarter) of the current CU, the vertical        transform is DCT-8 and DST-7, respectively. Otherwise, when a        sub-TU has a same height as the current CU, DCT-2 is used.    -   (c) MTS disabled in SPS: When sps_mts_enabled_flag is signaled        as true, but both sps_explicit_mts_intra_enabled_flag and        sps_explicit_mts_inter_enabled_flag are signaled as false, for        intra prediction residuals, the horizontal transform is selected        as DST-7 as long as the block width is greater than or equal to        4 and less than or equal to 16, and the vertical transform is        selected as DST-7 as long as the block height is greater than or        equal to 4 and less than or equal to 16.

A mode-dependent non-separable secondary transform (NSST), such as inVVC, can be applied between the forward core transform and quantization(at the encoder), and between the de-quantization and inverse coretransform (at the decoder). To keep complexity low, NSST can only beapplied to the low frequency coefficients after the primary transform.If both a width (W) and a height (H) of a transform coefficient block islarger than or equal to 8, then 8×8 non-separable secondary transformcan be applied to the top-left 8×8 region of the transform coefficientsblock. Otherwise, if either W or H of a transform coefficient block isequal to 4, a 4×4 non-separable secondary transform can be applied andthe 4×4 non-separable transform can be performed on the top-left min(8,W)×min(8, H) region of the transform coefficient block. The abovetransform selection rule can be applied for both luma and chromacomponents.

Matrix multiplication implementation of a non-separable transform can bedescribed as follows in formula (1) by using a 4×4 input block as anexample. To apply the non-separable transform, the 4×4 input block X

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & (1)\end{matrix}$

is represented as a vector

:

=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X ₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁X ₃₂ X ₃₃]^(T)

The non-separable transform can be calculated as

=T·

, where

indicates the transform coefficient vector, and T is a 16×16 transformmatrix. The 16×1 coefficient vector

is subsequently re-organized as 4×4 block using the scanning order forthat block (horizontal, vertical or diagonal). The coefficients withsmaller indices can be placed with the smaller scanning indices in the4×4 coefficient block. A Hypercube-Givens Transform (HyGT) withbutterfly implementation, such as in JEM, can be used instead of matrixmultiplication to reduce the complexity of the non-separable transform.

In one design of NSST, a total of 35×3 non-separable secondarytransforms can be applied for both 4×4 and 8×8 block sizes, where 35 isthe number of transform sets specified by the intra prediction mode,denoted as set, and 3 is the number of NSST candidates for each intraprediction mode. The mapping from the intra prediction mode to thetransform set is defined in Table 6 for example. The transform setapplied to luma/chroma transform coefficients can be specified by thecorresponding luma/chroma intra prediction modes, according to Table 6.For intra prediction modes larger than 34 (diagonal predictiondirection), the transform coefficient block can be transposedbefore/after the secondary transform at the encoder/decoder.

TABLE 6 Mapping from intra prediction mode to transform set index intromdoe set intro mode set 0 0 34 34 1 1 35 33 2 2 36 32 3 3 37 31 4 4 3830 5 5 39 29 6 6 40 28 7 7 41 27 8 8 42 26 9 9 43 25 10 10 44 24 11 1145 23 12 12 46 22 13 13 47 21 14 14 48 20 15 15 49 19 16 16 50 18 17 1751 17 18 18 52 16 19 19 53 15 20 20 54 14 21 21 55 13 22 22 56 12 23 2357 11 24 24 58 10 25 25 59 9 26 26 60 8 27 27 61 7 28 28 62 6 29 29 63 530 30 64 4 31 31 65 3 32 32 66 2 33 33 67 (LM) Null

For each transform set, the selected non-separable secondary transformcandidate can be further specified by the explicitly signalled CU-levelNSST index. The index may be signalled in a bitstream one time for eachintra CU after transform coefficients and truncated unary binarizationis used. The truncated value is 2 in case of planar or DC mode, and 3for angular intra prediction mode. This NSST index may be signalled onlywhen there is more than one non-zero coefficient in a CU. The defaultvalue may be zero when it is not signalled. A zero value of this syntaxelement may indicate that the secondary transform is not applied to thecurrent CU, values 1-3 indicate which secondary transform from the setshould be applied.

In some embodiments, NSST cannot be applied for a block coded withtransform skip mode. When the NSST index is signalled for a CU and notequal to zero, NSST is not used for a block with a component (e.g.,chroma component, or luma component) that is coded with transform skipmode in the CU. When a CU with blocks having all components are coded intransform skip mode or the number of non-zero coefficients ofnon-transform-skip mode CBs is less than 2, the NSST index is notsignalled for the CU.

A variant of NSST using transform zero-out scheme, namely Reduced SizeTransform (RST), which is also called Low-Frequency Non-SeparableSecondary Transform (LFNST) such as in VVC Draft 5, has been proposed inJVET-N0193. In RST, whether the intra prediction mode is Planar or DCcan be checked for entropy coding the transform index of NSST. Fourtransform sets can be applied, and each transform set can include threeRST transform cores. The three RST transform cores can be either size16×48 (or 16×64) (applied for a transform coefficient block with aheight and a width both being greater than or equal to 8) or 16×16(applied for a transform coefficient block with either a height or awidth being equal to 4). For notational convenience, the 16×48 (or16×64) transform is denoted as RST8×8 and the 16×16 transform is denotedas RST4×4. For RST8×8, the two alternatives using 16×64 transform coresand 16×48 transform cores are shown in FIG. 10 and FIG. 11,respectively. FIG. 10 shows a an RST using a 16×64 secondary transformcore. FIG. 11 shows an RST using a 16×48 secondary transform core. Thetransform using 16×48 transform cores is adopted in VVC Draft 5 forexample.

The index indicating the selection of LFNST kernel (e.g., lfnst_idx) canbe signaled at the end of CU-level syntax, as indicated in Table 7.Table 7 provides syntax at a CU-level.

TABLE 7 Syntax of signaling an index for selection of LFNST kernelcoding_unit( x0, y0, cbWidth, cbHeight, treeType ) { Descriptor ......   numSigCoeff = 0    numZeroOutSigCoeff = 0    transform_tree( x0, y0,cbWidth, cbHeight, treeType )    lfnstWidth = ( treeType = =DUAL_TREE_CHROMA ) ?         cbWidth / SubWidthC : cbWidth   lfnstHeight = ( treeType = = DUAL_TREE_CHROMA ) ?         cbHeight /SubHcightC : cbHeight    if( Min( lfnstWidth, lfnstHeight ) >= 4 &&sps_lfnst_enabled_flag = = 1 &&     CuPredModer[ x0 ][ y0 ] = =MODE_INTRA &&     IntraSubPartitionsSplitType = = ISP_NO_SPLIT &&    !intra_mip_flag[ x0 ][ y0 ] ) {     if( ( numSigCoeff > ( ( treeType= = SINGLE_TREE ) ? 2 : 1 ) ) &&      numZeroOutSigCoeff = = 0 )     lfnst_idx[ x0 ][ y0 ] ae(v)    }   }  } }

In some examples, a Reduced Transform (RT) maps an N dimensional vectorto an R dimensional vector in a different space, where R/N (R<N) is thereduction factor. The RST matrix is an R×N matrix as follows in formula(2):

$\begin{matrix}{T_{R \times N} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1\; N} \\t_{21} & t_{22} & t_{23} & \; & t_{2\; N} \\\; & \vdots & \; & \ddots & \vdots \\t_{R\; 1} & t_{R\; 2} & t_{R3} & \ldots & t_{R\; N}\end{bmatrix}} & (2)\end{matrix}$

where the R rows of the transform are R bases of the N dimensionalspace. The inverse transform matrix for RT is the transpose of itsforward transform. FIG. 12A is a schematic view of forward and transformand FIG. 12B is a schematic view of inverse reduced transform.

The RST8×8 with a reduction factor of 4(¼ size) can be applied. Hence,instead of 64×64, which is atypical 8×8 non-separable transform matrixsize, a 16×64 direct matrix is used. In other words, the 64×16 inverseRST matrix is used at the decoder side to generate core (primary)transform coefficients in 8×8 top-left regions. The forward RST8×8 uses16×64 (or 8×64 for 8×8 block) matrices so that the forward RST8×8produces non-zero coefficients only in the top-left 4×4 region withinthe given 8×8 region. In other words, if RST is applied then the 8×8region except the top-left 4×4 region can have only zero coefficients.For RST4×4, 16×16 (or 8×16 for a 4×4 block) direct matrix multiplicationcan be applied.

In addition, for RST8×8, to further reduce the transform matrix size,instead of using the whole top-left 8×8 coefficients as input forcalculating a secondary transform, the top-left three 4×4 coefficientscan be used as the input for calculating the secondary transform. FIGS.13A-13B show different alternatives of RST8×8. FIG. 13A shows an examplefor 16×64 transform matrices and the whole top-left 8×8 coefficients areapplied as input for calculating the secondary transform. FIG. 13B showsan example for 16×46 transform matrices and the top-left three 4×4coefficients are used as the input for calculating secondary transform.

In some embodiments, an inverse RST can be conditionally applied whenthe following two conditions are satisfied: (a) block size is greaterthan or equal to the given threshold (W>=4 && H>=4); and (b) transformskip mode flag is equal to zero. If both width (W) and height (H) of atransform coefficient block is greater than 4, then the RST8×8 isapplied to the top-left 8×8 region of the transform coefficient block.Otherwise, the RST4×4 is applied on the top-left min(8, W)×min(8, H)region of the transform coefficient block.

If the RST index is equal to 0, RST is not applied. Otherwise, if theRST index is equal to one, RST is applied, and a corresponding kernel(or transform set) can be chosen in accordance with the RST index.

Furthermore, RST can be applied for intra CU in both intra and interslices, and for both Luma and Chroma. If a dual tree is enabled, RSTindices for Luma and Chroma are signaled separately. For inter slice(the dual tree is disabled), a single RST index is signaled and used forboth luma and chroma components. When the ISP mode is selected, RST isdisabled, and RST index is not signaled.

In some embodiments, an RST matrix can be chosen from four transformsets, and each of the transform sets includes, or consists of, twotransforms. Which transform set is applied can be determined from anintra prediction mode as follows: (a) if one of three CCLM modes isindicated, transform set 0 is selected, or (b) otherwise, transform setselection is performed according to Table 8:

TABLE 8 The transform set selection table Tr. set IntraPredMode indexIntraPredMode < 0 1 0 <= IntraPredMode <= 1 0 2 <= IntraPredMode <= 12 113 <= IntraPredMode <= 23 2 24 <= IntraPredMode <= 44 3 45 <=IntraPredMode <= 55 2 56 <= IntraPredMode 1The index (i.e., IntraPredMode) to access Table 8 has a range of [−14,83], which is a transformed mode index used for wide angle intraprediction.

A Matrix-based intra prediction (MIP) mode can be provided such as inVVC. For predicting the samples of a rectangular block of width (W) andheight (H), MIP takes one line of H reconstructed neighbouring boundarysamples that are located to the left of the block, and one line of Wreconstructed neighbouring boundary samples above the block as input. Ifthe reconstructed samples are unavailable, they can be generated, forexample as it is done in the conventional intra prediction.

The generation of the prediction signal can be based on the followingthree steps:

(a) Out of the boundary samples, four samples in the case of W=H=4 andeight samples in all other cases are extracted by averaging.

(b) A matrix vector multiplication, followed by addition of an offset,is carried out with the averaged samples as an input. The result is areduced prediction signal on a subsampled set of samples in the originalblock.

(c) The prediction signal at the remaining positions is generated fromthe prediction signal on the subsampled set by linear interpolationwhich is a single step linear interpolation in each direction.

The matrices and offset vectors needed to generate the prediction signalare taken from three sets S₀, S₁, S₂ of matrices. The set S₀ includes,or consists of, 18 matrices A₀ ^(i), i∈{0, . . . , 17}. Each of thematrices has 16 rows, 4 columns, and 18 offset vectors b₀ ^(i), i∈{0, .. . , 17}. Each of the offset vectors b₀ ^(i) has a size 16. Matricesand offset vectors of the set S₀ are used for blocks of size 4×4. Theset S₁ includes, or consists of, 10 matrices A₁ ^(i), i∈{0, . . . , 9}.Each of the matrices has 16 rows, 8 columns, and 10 offset vectors b₁^(i), i∈{0, . . . , 9}. Each of the offset vectors b₁ ^(i) has a size16. Matrices and offset vectors of the set S₁ are used for blocks ofsizes 4×8, 8×4, and 8×8. Finally, the set S₂ includes, or consists of, 6matrices A₂ ^(i), i∈{0, . . . , 5}. Each of the matrices has 64 rows, 8columns, and 6 offset vectors b₂ ^(i), i∈{0, . . . , 5} of size 64.Matrices and offset vectors of the set S₂ or parts of these matrices andoffset vectors are used for all other block-shapes.

FIG. 14 is an illustration of an example MIP for 8×8 blocks. As shown inFIG. 14, given an 8×8 block, MIP takes four averages along each axis ofthe boundary. The resulting eight input samples enter the matrix vectormultiplication. The matrices are taken from the set S₁. This yields 16samples on the odd positions of the prediction block. Thus, a total of(8*16)/(8*8)=2 multiplications per sample are performed. After adding anoffset, these samples are interpolated vertically by using the reducedtop boundary. Horizontal interpolation follows by using the originalleft boundary. The interpolation process does not require anymultiplications in this case.

In terms of signaling of MIP mode, for each CU in intra mode, a flagindicating whether an MIP mode is applied on the corresponding PU or notcan be sent in the bitstream. If an MIP mode is applied, the indexpredmode of the MIP mode can be signaled using an MPM-list including 3MPMs.

The derivation of the MPMs can be performed using the intra-modes of theabove and the left PU as follows. There are three fixed mapping tablesmap_angular_to_mip_(idx), idx∈{0,1,2}, and each table can be associatedwith a conventional intra prediction mode predmode_(Angular) with aspecific MIP mode, as described in the following formula (3).

predmode_(MIP)=map_angular_to_mip[predmode_(Angular)]  (3)

where map_angular_to_mip is a fixed look-up table. The index of themapping table can be decided based on the width (W) and height (H) ofPU, and in total three indices are available, as described below informula (4)

idx(PU)=idx(W,H)∈{0,1,2}  (4)

The formula (4) indicates from which of the three sets the MIPparameters are to be taken.

To generate the MPM list for a current block which is coded by MIP mode,an above MIP mode, namely mode_(MIP) ^(above), and a left MIP mode,namely mode_(MIP) ^(left), are firstly derived. The value of mode_(MIP)^(above) can be derived as follows:

(a) If the above PU PU_(above) is available, and it belongs to the sameCTU where the current PU resides, and PU_(above) is coded by MIP usingan MIP mode predmode_(MIP) ^(above) and idx(PU)=idx(PU_(above)),

mode_(MIP) ^(above)=predmode_(MIP) ^(above)  (5)

(b) If the above PU PU_(above) is available, and it belongs to the sameCTU where the current PU resides, and PU_(above) is coded using aconventional intra prediction mode predmode_(Angular) ^(above),

mode_(MIP) ^(above)=map_angular_to_mip[predmode_(Angular) ^(above)]  (6)

(c) Otherwise,

mode_(MIP) ^(above)=−1  (7)

which means that this mode is unavailable. The value of mode_(MIP)^(left) can be derived in the same way as deriving mode_(MIP) ^(above)but without checking whether the left PU belongs to the same CTU wherethe current PU resides.

Finally, given the derived mode_(MIP) ^(above) and mode_(MIP) ^(left)and three pre-defined fixed default MPM lists list_(idx), idx∈{0,1,2},where each of the MPM lists contains three distinct MIP modes, an MPMlist is constructed. The MPM list can be constructed based on the givendefault list list_(idx(PU)) and mode_(MIP) ^(above) and mode_(MIP)^(left), by substituting −1 by default values as well as removingduplicate MIP modes.

Exemplary flags for signaling MIP modes are illustrated in Table 9 whichis a CU-level syntax table.

TABLE 9 Syntax of flags signaling MIP modes at CU-level coding_unit( x0,y0, cbWidth, cbHeight, treeType ) { Descriptor ......      if(sps_mip_enabled_flag &&       ( Abs( Log2( cbWidth ) − Log2( cbHeight )) <= 2 ) &&        cbWidth <= MaxTbSizeY && cbHeight <= MaxTbSizeY )      intra_mip_flag[ x0 ][ y0 ] ae(v)      if( intra_mip_flag[ x0 ][ y0] ) {        intra_mip_mpm_flag[ x0 ][ y0 ] ae(v)       if(intra_mip_mpm_flag[ x0 ][ y0 ] )        intra_mip_mpm_idx[ x0 ][ y0 ]ae(v)       else        intra_mip_mpm_remainder[ x0 ][ y0 ] ae(v)      }else {       if( sps_mrl_enabled_flag && ( ( y0 % CtbSizeY ) > 0 ) )       intra_luma_ref_idx[ x0 ][ y0 ] ae(v)       if(sps_isp_enabled_flag && intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&        (cbWidth <= MaxTbSizeY && cbHeight <= MaxTbSizeY ) &&        ( cbWidth *cbHeight > MinTbSizeY * MinTbSizeY ) )       intra_subpartitions_mode_flag[ x0 ][ y0 ] ae(v)       if(intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 1 &&        cbWidth <=MaxTbSizeY && cbHeight <= MaxTbSizeY )       intra_subpartitions_split_flag[ x0 ][ y0 ] ae(v)       if(intra_luma_ref_idx[ x0 ][ y0 ] ) = = 0 &&       intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0 )       intra_luma_mpm_flag[ x0 ][ y0 ] ae(v)       if(intra_luma_mpm_flag[ x0 ][ y0 ] ) {        if( intra_luma_ref_idx[ x0 ][y0 ] = = 0 )         intra_luma_not_planar_flag[ x0 ][ y0 ] ae(v)       if(intra_luma_not_planar_flag[ x0 ][ y0 ] )        intra_luma_mpm_idx[ x0 ][ y0 ] ae(v)       } else       intra_luma_mpm_remainder[ x0 ][ y0 ] ae(v)      }     }    }......

In some embodiments, the MIP modes can be harmonized with the MPM-basedcoding of the conventional intra-prediction modes as follows. The lumaand chroma MPM-list derivation processes for the conventionalintra-prediction modes use separate fixed tablesmap_mip_to_angular_(idx), idx∈{0,1,2}, which map an MIP-modepredmode_(MIP) to one of the conventional intra-prediction modes

predmode_(Angular)=map_mip_to_angular[predmode_(MIP)]  (8)

where map_mip_to_angular is a fixed look-up table. For the luma MPM-listderivation, whenever a neighboring luma block is coded by an MIP modepredmode_(MIP), this block can be treated as if it was using theconventional intra-prediction mode predmode_(Angular). For the chromaMPM-list derivation, whenever the current luma block uses an MIP-mode,the same mapping can be used to translate the MIP-mode to a conventionalintra prediction mode.

Exemplary intra prediction modes are illustrated in FIG. 15. A total of35 intra prediction modes is illustrated in FIG. 15, for example as usedin HEVC. Among the 35 intra prediction modes, mode 10 is a horizontalmode and mode 26 is a vertical mode. Modes 2, 18, and 34 are diagonalmodes. The 35 intra prediction modes can be signalled by three mostprobable modes (MPMs) and 32 remaining modes.

A total of 95 intra prediction modes is illustrated in in FIG. 16, forexample as used in VVC. Mode 18 is a horizontal mode and mode 50 is avertical mode. Modes 2, 34, and 66 are diagonal modes. Modes −1 to −14and Modes 67 to 80 can be referred to as Wide-Angle Intra Prediction(WAIP) modes.

Position dependent prediction combination (PDPC), such as in VVC, can beapplied to the following intra modes without signaling: planar, DC, WAIPmodes, horizontal, vertical, bottom-left angular mode (mode 2), 8adjacent angular modes (mode 3˜10) of the bottom-left angular mode,top-right angular mode (mode 66), and 8 adjacent angular modes (mode58˜65) of the top-right angular mode. A prediction sample pred(x,y)located at position (x, y) of a current block can be predicted using anintra prediction mode (e.g., DC, planar, angular) and a linearcombination of reference samples according to the PDPC expression thatis shown in formula (9).

pred(x,y)=(wL×R _(−1,y) +wT×R _(x,−1) −wTL×R_(−1,−1)+(64−wL−wT+wTL)×pred(x,y)+32)>>6  (9)

where R_(x,−1) and R_(−1,y) represent reference samples located at thetop and left of a current sample (x, y), respectively, and R_(−1,−1)represents a reference sample located at the top-left corner of thecurrent block.

The weights applied in the DC mode can be calculated according toformula (10) for a block with a width and a height.

wT=32>>((y<<1)>>nScale), wL=32>>((x<<1)>>nScale),wTL=(wL>>4)+(wT>>4)  (10)

In formula (10), nScale=(log 2(width)−2+log 2(height)−2+2)>>2, wTdenotes the weighting factor for the reference sample located in theabove reference line with the same horizontal coordinate, wL denotes theweighting factor for the reference sample located in the left referenceline with the same vertical coordinate, and wTL denotes the weightingfactor for the top-left reference sample of the current block. nScalecan specify how fast the weighting factors (e.g., wL, wTL, and wT)decrease along the axis (wL decreasing from left to right or wTdecreasing from top to bottom), and denote a weighting factor decrementrate. The weighting factor decrement rate weighting factor decrementrate nScale is the same along x-axis (from left to right) and y-axis(from top to bottom) in VVC. In addition, 32 denotes the initialweighting factors for the neighboring samples, and the initial weightingfactors are also the top (left or top-left) weightings assigned totop-left samples in current CB. The weighting factors of neighboringsamples in a PDPC process should be equal to or less than the initialweighting factors.

In some embodiments, wTL=0 in Planar mode, wTL=wT in horizontal mode,and wTL=wL in vertical mode. The PDPC weights (or weighting factors) canbe calculated with adds and shifts. The value of pred(x, y) can becomputed in a single step using formula (9) for example.

FIG. 17A illustrates the PDPC weights (wL, wT, wTL) in DC mode for asample 1702 located in (0, 0) inside a 4×4 block 1700. As shown in FIG.17A, wL=32, wT=32, and wTL=−4. FIG. 17B illustrates the PDPC weights(wL, wT, wTL) in DC mode for a sample 1704 located in (1, 0) inside the4×4 block 1700. As shown in FIG. 17B, wL=8, wT=32, and wTL=−2. If PDPCis applied to DC, planar, horizontal, or vertical intra modes,additional boundary filters are not needed, such as the HEVC DC modeboundary filter or horizontal/vertical mode edge filters.

FIG. 17A can also illustrate the definition of reference samplesR_(x,−1), R_(−1,y), and R_(−1,−1) when PDPC is applied to the top-rightdiagonal mode. The prediction sample pred(x′, y′) is located at (x′, y′)within the prediction block (or the 4×4 block) 1700. The coordinate x ofthe reference sample R_(x,−1) is given by: x=x′+y′+1, and the coordinatey of the reference sample R_(−1,y) is similarly given by: y=x′+y′+1.

The following clause describes an example of the PDPC, such as in VVCdraft 2, where nScale is used to specify the weighting factor decrementrate, and “32” in formulas (14), (15), (19), and (20) specifies theinitial weighting factors. Inputs to the position-dependent intraprediction combination process can include: the intra prediction modepredModeIntra; a variable nTbW specifying the transform block width; avariable nTbH specifying the transform block height; a variable refWspecifying the reference samples width; a variable refH specifying thereference samples height; the predicted samples predSamples[x][y], withx=0 . . . nTbW−1 and y=0 . . . nTH−1; the neighbouring samples p[x][y],with

x=−1, y=−1 . . . refH−1 and x=0 . . . refW−1, y=−1; and a variable cIdxspecifying the colour component of the current block.

Outputs of the position-dependent intra prediction combination processcan include the modified predicted samples predSamples[x][y] with

x=0 . . . nTbW−1, y=0 . . . nTbH−1. Depending on the value of cIdx, thefunction clip1Cmp can set as follows. If cIdx is equal to 0, clip1Cmpcan beset equal to Clip1Y. Otherwise, clip1Cmp can be set equal toClip1C. The variable nScale can be set to ((Log 2(nTbW)+Log2(nTbH)−2)>>2).

The reference sample arrays mainRef[x] and sideRef[y], with x=0 . . .refW and y=0 . . . refH can be derived as follows:

mainRef[x]=p[x][−1]

sideRef[y]=p[−1][y]  (11)

The variables refL[x][y], refT[x][y], wT[y], wL[y] and wTL[x][y] withx=0 . . . nTbW−1, y=0 . . . nTbH−1 can be derived as follows. IfpredModeIntra is equal to INTRA_PLANAR, INTRA_DC, INTRA_ANGULAR18, orINTRA_ANGULAR50, the following applies:

refL[x][y]=p[−1][y]  (12)

refT[x][y]=p[x][−1]  (13)

wT[y]=32>>((y<<1)>>nScale)  (14)

wL[x]=32>>((x<<1)>>nScale)  (15)

wTL[x][y]=(predModeIntra==INTRA_DC)?((wL[x]>>4)+(wT[y]>>4)):0  (16)

Otherwise, if predModeIntra is equal to INTRA_ANGULAR2 orINTRA_ANGULAR66, the following applies:

refL[x][y]=p[−1][x+y+1]  (17)

refT[x][y]=p[x+y+1][−1]  (18)

wT[y]=(32>>1)>>((y<<1)>>nScale)  (19)

wL[x]=(32>>1)>>((x<<1)>>nScale)  (20)

wTL[x][y]=0  (21)

Otherwise, if predModeIntra is less than or equal to INTRA_ANGULAR10,the following ordered steps apply:

The variables dXPos[y], dXFrac[y], dXInt[y] and dX[y] are derived asfollows using invAngle depending on intraPredMode:

dXPos[y](((y+1)*invAngle+2)>>2

dXFrac[y]=dXPos[y]&63

dXInt[y]=dXPos[y]>>6

dX[y]=x+dXInt[y]  (22)

The variables refL[x][y], refT[x][y], wT[y], wL[y] and wTL[x][y] arederived as follows:

refL[x][y]=0  (23)

refT[x][y]=(dX[y]<refW−1)?((64−dXFrac[y])*mainRef[dX[y]]+dXFrac[y]*mainRef[dX[y]+1]+32)>>6:0  (24)

wT[y]=(dX[y]<refW−1)?32>>((y<<1)>>nScale):0  (25)

wL[x]=0  (26)

wTL[x][y]=0  (27)

Otherwise, if predModeIntra is greater than or equal to INTRA_ANGULAR58,the following ordered steps apply:

The variables dYPos[x], dYFrac[x], dYInt[x] and dY[x] are derived asfollows using invAngle depending on intraPredMode:

dYPos[x]=((x+1)*invAngle+2)>>2

dYFrac[x]=dYPos[x]&63

dYInt[x]=dYPos[x]>>6

dY[x]=x+dYInt[x]  (28)

The variables refL[x][y], refT[x][y], wT[y], wL[y] and wTL[x][y] arederived as follows:

refL[x][y]=(dY[x]<refH−1)?((64−dYFrac[x])*sideRef[dY[x]]+dYFrac[x]*sideRef[dY[x]+1]+32)>>6:0  (29)

refT[x][y]=0  (30)

wT[y]=0  (31)

wL[x]=(dY[x]<refH−1)?32>>((x<<1)>>nScale):0  (32)

wTL[x][y]=0  (33)

Otherwise, refL[x][y],refT[x][y], wT[y], wL[y] and wTL[x][y] are all setequal to 0.

The values of the filtered samples filtSamples[x][y], with x=0 . . .nTbW−1, y=0 . . . nTbH−1 can derived as follows:

filtSamples[x][y]=clip1Cmp((refL[x][y]*wL+refT[x][y]*wT−p[−1][−1]*wTL[x][y]+(64−wL[x]−wT[y]+wTL[x][y])*predSamples[x][y]+32)>>6)

For the chroma component of an intra coded block, the encoder selectsthe best chroma prediction modes among five modes including Planar (modeindex 0), DC (mode index 1), Horizontal (mode index 18), Vertical (modeindex 50), Diagonal (mode index 66), and a direct copy of the intraprediction mode for the associated luma component, namely DM mode. Anexample eof the mapping between intra prediction direction and intraprediction mode number for chroma is shown in Table 10.

TABLE 10 Mapping between intra prediction direction and intra predictionmode for chroma IntraPredModeY[ xCb + cbWidth/2 ][ yCb +intra_chroma_pred_ cbHeight/2 ] mode[ xCb ][ yCb ] 0 50 18 1 X ( 0 <= X<= 66) 0 66 0 0 0 0 1 50 66 50 50 50 2 18 18 66 18 18 3 1 1 1 66 1 4 050 18 1 XAs shown in Table 10, the intra prediction directions for a chromacomponent can be indicated using a syntax element intra_chroma_pred_mode[xCb][yCb], which can have five values (e.g., 0-5), and each value canindicate a respective intra prediction direction for the chromacomponent. A syntax elementIntraPredModeY[xCb+cbWidth/2][yCb+cbHeight/2] can indicate correspondingintra prediction modes for the chroma component responsive to the intraprediction directions for chroma component.

To avoid a duplicate mode, the four modes other than DM can be assignedaccording to the intra prediction mode of the associated luma component.When the intra prediction mode number for the chroma component is 4, theintra prediction direction for the luma component can be used for theintra prediction sample generation for the chroma component. When theintra prediction mode number for the chroma component is not 4 and isidentical to the intra prediction mode number for the luma component,the intra prediction direction of 66 can be used for the intraprediction sample generation for the chroma component.

Merge mode for inter-picture prediction indicates that the motion datais inferred instead of being explicitly signaled for a block. A mergecandidate list of candidate motion parameters can be firstlyconstructed, and then an index can be signaled to identify whichcandidate in the merge candidate list is to be used.

The merge candidate list can include a non sub-CU merge candidate listand a sub-CU merge candidate list. The non sub-CU merge candidates canbe constructed based on the spatial neighboring motion vectors,collocated temporal motion vectors, and history based motion vectors.The sub-CU Merge candidate list can include affine merge candidates andATMVP merge candidates. A sub-CU merge candidate can be used to derivemultiple MVs for a current CU, and a different part of the samples inthe current CU can have different motion vectors.

Skip mode for inter-picture prediction indicates that the motion datafor a block is inferred instead of being explicitly signaled, and thatthe prediction residual is zero, i.e., no transform coefficients aretransmitted. At the beginning of each CU in an inter-picture predictionslice, a skip_flag can be signaled that implies: (a) the merge mode isused to derive the motion data; and (b) no residual data is present inthe bitstream.

Multi-hypothesis intra-inter prediction (also referred to as combinedintra-inter prediction (CIIP) mode) combines one intra prediction andone merge indexed prediction (or one inter prediction in merge mode),namely intra-inter prediction mode. When a CU is coded in the mergemode, and if the CU contains at least 64 luma samples (i.e., CU widthtimes CU height is equal to or larger than 64), an additional flag canbe signaled to indicate if the combined inter/intra prediction (CIIP)mode is applied to the CU. The additional flag can be signaled to selectan intra mode from an intra candidate list when the additional flag istrue. For a luma component of the CU, the intra candidate list can bederived from 4 intra prediction modes including DC, planar, horizontal,and vertical modes, and the size of the intra candidate list can be 3 or4 depending on the block shape. When the CU width is larger than adouble value of CU height, horizontal mode is removed from the intramode list. When the CU height is larger than the double value of CUwidth, vertical mode is removed from the intra mode list. Further, oneintra prediction mode selected by the intra mode index and one mergeindexed prediction selected by the merge index can be combined using aweighted average. For a chroma component of the CU, DM can be alwaysapplied without extra signaling.

The weights (or weighting factors) for combining predictions can bedescribed as follows. When DC or planar mode is selected or a CodingBlock (CB) with a width or a height smaller than 4, equal weights areapplied. For a CB with a width and a height larger than or equal to 4,when horizontal/vertical mode is selected, the CB is firstvertically/horizontally split into four equal-area regions. Each weightset, denoted as (w_intra_(i), w_inter_(i)), where i is from 1 to 4 and(w_intra₁, w_inter₁)=(6, 2), (w_intra₂, w_inter₂)=(5, 3), (w_intra₃,w_inter₃)=(3, 5), and (w_intra₄, w_inter₄)=(2, 6), can be applied to acorresponding region. (w_intra₁, w_inter₁) is applied to a regionclosest to the reference samples and (w_intra₄, w_inter₄) is applied toa region farthest away from the reference samples. Then, the combinedprediction can be calculated by summing up the two weighted predictions(e.g., the inter prediction and the intra prediction in merge mode) andright-shifting 3 bits. Moreover, the intra prediction mode for the intrahypothesis of predictors can be saved for the intra mode coding of thefollowing neighboring CBs if they are intra coded.

Inter PDPC mode can apply a PDPC filtering process directly to interprediction samples (or reconstructed samples of an inter coded CU), suchas in VVC. One flag, namely interPDPCFlag, can be signaled to indicatewhether to apply the PDPC filtering process or not. When interPDPCFlagis true, the prediction samples (or reconstructed samples of an intercoded CU) are further modified in the PDPC process. Inter PDPC mode canbe combined with any inter coded modes to further improve the interprediction samples. However, in some embodiments, restrictions can beapplied to prohibit the inter PDPC modes from comingling with certaininter coded modes. In one example, inter PDPC mode can only be appliedto regular merge mode and/or sub-block merge mode. In another example,inter PDPC mode cannot be applied to merge skip mode.

A triangle partition mode for inter prediction, such as in VTM3, canonly be applied to CUs that are 8×8 or larger and are coded in skip ormerge mode. For a CU satisfying these conditions, a CU-level flag can besignalled to indicate whether the triangle partition mode is applied ornot. When the triangle partition mode is applied, a CU can be splitevenly into two triangle-shaped partitions, using either the diagonalsplit or the anti-diagonal split that are illustrated for example inFIG. 18A and FIG. 18B respectively. Each triangle partition in the CUcan be inter-predicted using its own motion. In addition, only auni-prediction can be allowed for each partition. That is, eachpartition can have one motion vector and one reference index. Theuni-prediction motion constraint can be applied to ensure that, same asa conventional bi-prediction, only two motion compensated predictionsare needed for each CU. The uni-prediction motion for each partition canbe derived from a uni-prediction candidate list that can be constructedusing a construction process. In the construction process, theuni-prediction candidate list can include five uni-prediction motionvector candidates. The uni-prediction candidate list can be derived fromseven neighboring blocks including five spatial neighboring blocks andtwo temporal co-located blocks.

If the CU-level flag indicates that the current CU is coded using thetriangle partition mode, an index (or triangle partition index) in therange of [0, 39] can be further signalled. Using the triangle partitionindex, a direction of the triangle partition (e.g., diagonal oranti-diagonal), as well as a motion for each of the partitions can beobtained through a look-up table. After each of the triangle partitionsis predicted, the sample values along the diagonal or anti-diagonal edgecan be adjusted using a blending processing with adaptive weights.Accordingly, the prediction signal for the whole CU can be obtained. Atransform and quantization process can further be applied to the wholeCU as in other prediction modes. Finally, the motion field of a CU thatis predicted using the triangle partition mode can be stored in 4×4units.

Embodiments of the present disclosure include implicit transformselection methods for an inter PDPC prediction mode. The method can bebased on inter PDPC mode and a CIIP mode, for example as proposed forVVC.

In a case that MTS is not used (e.g., disabled by high level syntax(HLS) indicating MTS cannot be applied for coding the current bitstreamsegment) or an ISP prediction mode is applied, an implicit MTS methodcan be used such as in VVC. When implicit MTS is enabled, for an intraprediction residual, the horizontal transform can be set as DST-7 aslong as the block width is smaller than or equal to 16 and greater thanor equal to 4, the vertical transform can be set as DST-7 as long as theblock height is smaller than or equal to 16 and greater than or equal to4.

Since inter PDPC mode can be combined with different modes of aninter-coded CU, such as regular merge mode or sub-block merge mode, theenergy distribution of inter predicted residuals after applying a PDPCfilter can be different for different modes. Therefore, differenttransform designs should be considered for the different combinations ofinter PDPC mode and other inter modes. The consideration of differenttransform designs has not been addressed for inter PDPC mode.

In the disclosure, inter PDPC mode and/or CIIP mode can generateprediction residuals which have similar statistics of an intraprediction residual. Therefore, DST-7 may be a more efficient transformother than DCT-2. In some embodiments, DST-4 may be used to replaceDST-7 for certain small block sizes or all block sizes. Further, in someembodiments, PDPC refers to simplied PDPC.

In the disclosure, the transform design used for inter predictedresiduals after applying the PDPC filter can be dependent on the codedinformation of a current block and neighboring blocks of the currentblock, which includes but is not limited to inter prediction mode, mergeflag, block size, color component, etc.

In one embodiment, when the inter PDPC mode is on, sub-block transform(SBT) is always on/off regardless which inter coded modes the inter PDPCis applied to. In another embodiment, when inter PDPC is applied tosub-block merge mode, SBT is allowed. Otherwise, when inter PDPC isapplied to the merge mode except the sub-block merge mode, SBT is alwaysoff. In another embodiment, when inter PDPC is applied to triangle mergemode, SBT is allowed. Alternatively, when interPDPC is applied totriangle merge mode, SBT is not allowed.

In another embodiment, when inter PDPC mode is on, only a subset of SBTtypes can be allowed. In a first example, when the inter PDPC mode and aSBT flag are both on, the residual partition (e.g., partition that isallowed to have non-zero coefficients) of the current CU is always therightmost or bottommost partition. In a second example, when the interPDPC mode and the SBT flag are both on, the leftmost or topmostpartition of the current CU is always the zero-residual partition.

In another embodiment, when the inter PDPC mode is on, only a subset ofavailable transform types can be used. In a first example, when the PDPCmode is on, type-8 discrete cosine transform (DCT-8) is excluded fromthe allowed transform types. For example, when the PDPC mode is on, onlytype-2 discrete cosine transform (DCT-2) and type-7 discrete sinetransform (DST-7) can be used for the inter predicted residuals. In asecond example, when the PDPC mode is on, DST-7 is excluded from theallowed transform types. For example, when the PDPC mode is on, onlyDCT-2 and DCT-8 can be used for the inter predicted residuals. In athird example, when the PDPC mode is on, only DST-7 can be applied.

In a fourth example, when the inter PDPC mode is on, DST-7 is alwaysused as both the horizontal and vertical transform for some block sizes,and DCT-2 is used as both the horizontal and vertical transform forother block sizes. In a first embodiment, implicit transform scheme (ormode) is applied for the inter PDPC mode. For example, the horizontaltransform is set as DST-7 as long as the block width is smaller than orequal to a threshold T, and the vertical transform is set as DST-7 aslong as the block height is smaller than or equal to the threshold T.Example values of the threshold T include, but are not limited to 4pixels, 8 pixels, 16 pixels, and 32 pixels. In a second embodiment,implicit transform scheme can only be applied for a luma component ofthe current CU, and only DCT-2 and/or TSM can be applied for a chromacomponent of the current CU.

In another embodiment, when the inter PDPC mode is on, in addition toTSM, two transform schemes can be applied for the prediction residualand the selection is signaled. In an example, the two transform schemescan include: (1) DCT-2 as both horizontal and vertical transforms, and(2) DST-7 as both horizontal and vertical transforms.

In yet another one embodiment, when inter PDPC mode is on, MTS is alwayson/off regardless which inter coded modes the inter PDPC is applied to.

A selection of a context that is applied to entropy code an index fortransform signaling (e.g., a flag/index indicating whether or which ofDCT2, TSM, DST7, DCT8 is applied) can depend on whether the CIIP isapplied for current block, and/or whether the inter PDPC mode is appliedfor a current block.

The flag of the inter PDPC mode can be context coded and the contextused can be dependent on the coded information of a current block andneighboring blocks of the current block, including but not limited tointra-inter flag, intra mode flag, inter mode flag, skip flag, mergeflag, inter PDPC flag, etc. In one embodiment, only one context is usedfor the entropy coding of inter PDPC mode. In another embodiment, Mcontexts are used for the entropy coding of inter PDPC mode. M can beany positive integer greater than 1, such as 2 or 3. In a first example,if one of the neighboring modes is intra coded, intra-inter coded, orinter PDPC coded, a first context is used. Otherwise, a second contextis used. In a second example, if both neighboring modes are intra coded,intra-inter coded, or inter PDPC coded, the first context is used.Otherwise if only one of the neighboring modes is intra coded,intra-inter coded, or inter PDPC coded, the second context is used.Otherwise, none of the neighboring modes is intra coded, intra-intercoded, or inter PDPC coded the third context is used.

In some embodiments, the inter PDPC mode cannot be used together withIntra Block Copy (IBC) mode.

In the disclosure, the weightings applied in the inter PDPC mode (e.g.,wL, wT and/or wTL) can depend on coded information, including whether aneighboring block is coded by intra-inter mode, intra prediction mode,inter prediction mode, skip mode, merge mode, or inter PDPC mode.

An implicit transform scheme can be used for prediction residuals ofCIIP. In one embodiment, for prediction residuals of CIIP, thehorizontal transform can be set as DST-7 as long as the block width issmaller than or equal to a threshold T, and the vertical transform canbe set as DST-7 as long as the block height is smaller than or equal tothe threshold T. Example values of the threshold T include, but are notlimited to 4 pixels, 8 pixels, 16 pixels, and 32 pixels. In oneembodiment, the transform selection of CIIP can depend on the weightingsbetween intra prediction part (w_(intra)) and inter prediction part(w_(inter)). In one example, if w_(intra)/w_(inter) is larger than agiven threshold T1, the horizontal transform is set as DST-7 as long asthe block width is smaller than or equal to a threshold T2, and thevertical transform is set as DST-7 as long as the block height issmaller than or equal to the threshold T2. Example values of the T1 caninclude, but are not limited to 2, 2.5, 3, and 7. Example values of theT2 can include, but are not limited to 4 pixels, 8 pixels, 16 pixels,and 32 pixels.

In one embodiment, the transform selection of CIIP can depend on thenumber of intra coded neighboring blocks. In a first example, if boththe above and left neighboring blocks are intra coded, the horizontaltransform is set as DST-7 as long as the block width is smaller than orequal to a threshold T2, and the vertical transform is set as DST-7 aslong as the block height is smaller than or equal to a threshold T2.Otherwise, DCT2 is used as the horizontal and vertical transforms.Example values of the T2 include, but are not limited to 4 pixels, 8pixels, 16 pixels, and 32 pixels. In a second example, if more than N ofthe above and left neighboring blocks are intra coded, the horizontaltransform is set as DST-7 as long as the block width is smaller than orequal to a threshold T2, and the vertical transform is set as DST-7 aslong as the block height is smaller than or equal to a threshold T2.Otherwise, DCT2 is used as the horizontal and vertical transforms.Example values of the T2 include, but are not limited to 4 pixels, 8pixels, 16 pixels, and 32 pixels. Example values of N include, but arenot limited to 1, 2, 3, and 4.

In the disclosure, the weightings (or weighting factors) applied onintra prediction part (w_(intra)) and weightings applied on interprediction part (w_(inter)) in CIIP can also depend on whetherneighboring blocks are coded using the CIIP mode and/or the inter PDPCmode. In one embodiment, if both the top-right (or top) and bottom-left(or left) neighboring blocks are coded using the CIIP mode, thew_(intra) is assigned as a first value (e.g., 3). If one of thetop-right and bottom-left neighboring blocks are coded using the CIIPmode, the w_(intra) is assigned as a second value (e.g., 2). If none ofthe top-right and bottom-left neighboring blocks are coded using theCIIP mode, then the w_(intra) is assigned as a third value (e.g., 1).The value of w_(inter) can be assigned according to w_(intra), e.g.,w_(inter)=N−w_(intra). Example values of N include but are not limitedto 2, 4, 8, and 16. In one embodiment, if both the top-right (or top)and bottom-left (or left) neighboring blocks are coded using the interPDPC mode, then the w_(intra) is assigned as a first value (e.g., 3). Ifone of the top-right and bottom-left neighboring blocks are coded usingthe inter PDPC mode, then the w_(intra) is assigned as a second value(e.g., 2). If none of the top-right and bottom-left neighboring blocksare coded using the inter PDPC mode, the w_(intra) is assigned as athird value (e.g., 1). The value of w_(inter) can be assigned accordingto w_(intra), e.g., w_(inter)=N−w_(intra). Example values of N includebut are not limited to 2, 4, 8, and 16.

In the disclosure, if a filtering process is applied on the interprediction block and the filtering process uses the neighboringreconstructed samples to further adjust the inter prediction samples ofthe current block, a default primary transform can be applied. In oneembodiment, the pre-defined primary transform is DST-7 for bothhorizontal and vertical transforms. In one embodiment, the pre-definedprimary transform is DCT-2 for both horizontal and vertical transforms.In one embodiment, the pre-defined horizontal primary transform is DST-7as long as the block width is smaller than or equal to a threshold T.Otherwise, DCT-2 is used. Example values of the threshold T include, butare not limited to 4 pixels, 8 pixels, 16 pixels, and 32 pixels. In oneembodiment, the pre-defined vertical primary transform is DST-7 as longas the block height is smaller than or equal to the threshold T.Otherwise, DCT-2 is used.

In one embodiment, the filtering process can be a boundary filteringprocess, in which only a few of first rows and/or a few of first columnsof inter prediction samples that are adjacent to the boundary of a interprediction block can be further adjusted using the neighboringreconstructed samples, but the whole inter prediction block is notmodified. In one embodiment, the filtering process can applyposition-dependent weightings between the inter prediction samples andthe neighboring reconstructed samples used for the filtering. In oneembodiment, implicit transform scheme can only be applied for a lumacomponent of the inter prediction block, and only DCT-2 and/or TSM canbe applied for a chroma component of the inter prediction block. In oneembodiment, MTS is not signaled when the filtering process is applied.In a first example, the filtering process refers to the inter-PDPC mode.In a second example, the filtering process refers to the CIIP mode.

Embodiments of the present disclosure include modifications to animplicit transform. The semantics of MTS related syntax elements, suchas in VVC, can be confusing. For example, to enable explicit intra MTS,both sps_mts_enabled_flag and sps_explicit_mts_intra_enabled_flag needto be 1. However, to enable implicit MTS, sps_mts_enabled_flag needs tobe 1 but sps_explicit_mts_intra_enabled_flag needs to be 0. In anotherexample, to enable explicit inter MTS, both sps_mts_enabled_flag andsps_explicit_mts_inter_enabled_flag need to be 1, but only one codingtool (or one syntax element) is under control.

In the disclosure, MTS selection for intra prediction residual (whetherDCT-2, implicit MTS or explicit intra MTS) and inter prediction residual(whether DCT-2, or explicit inter MTS and implicit MTS for SBT) can beindicated using separate syntax elements.

In one embodiment, the following HLS syntaxes are designed forindicating the usage of MTS, as shown in Table 11 for example.

TABLE 11 Syntaxes elments indicating the usage of MTSseq_parameter_set_rbsp( ) { Descriptor ......  sps_intra_mts_selectionue(v)  sps_inter_mts_selection_flag u(1) ......As shown in Table 11, sps_intra_mts_selection can have a value of 0, 1,and 2. When sps_intra_mts_selection is equal to 0 or 1, tu_mts_idx isnot present in the transform unit syntax for intra coding units. Whensps_intra_mts_selection is equal to 2, tu_mts_idx can be present in thetransform unit syntax for intra coding units. Moreover, whensps_intra_mts_selection is equal to 0, implicit MTS is not applied forintra prediction residuals. When sps_intra_mts_selection is equal to 1,implicit MTS is applied for intra prediction residuals.sps_inter_mts_selection_flag can have a value of 0 and 1. Whensps_inter_mts_selection_flag is equal to 1, tu_mts_idx can be present inthe transform unit syntax for inter coding units. Whensps_inter_mts_selection_flag is equal to 0, tu_mts_idx is not present inthe transform unit syntax for inter coding units. Exemplary syntaxdesigned for indicating the usage of MTS based on the syntax elements inTable 11 is shown in Table 12.

TABLE 12 Syntaxes designed for indicating usage of MTS if( ( (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTER && sps_inter_mts_selection_flag )  || ( CuPredMode[ chType ][ x0 ][ y0 ] == MODE_INTRA &&  sps_intra_mts_selection = = 2) ) &&  (!transform_skin_flag[ x0 ][ y0 ] ) )  tu_mts_idx[ x0 ][ y0 ] ae(v)

An example of a modified transformation process for scaled transformcoefficients according to some embodiments is described below. Inputs tothis process can include a luma location (xTbY, yTbY) specifying thetop-left sample of the current luma transform block relative to thetop-left luma sample of the current picture; a variable nTbW specifyingthe width of the current transform block; a variable nTbH specifying theheight of the current transform block; a variable cIdx specifying thecolour component of the current block; and/or an (nTbW)×(nTbH) arrayd[x][y] of scaled transform coefficients with x=0 . . . nTbW−1, y=0 . .. nTbH−1. An output of this process is the (nTbW)×(nTbH) array r[x][y]of residual samples with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

The variable implicitMtsEnabled can be derived as follows. If one of aplurality of conditions is true, implicitMtsEnabled is set equal to 1.The plurality of conditions can include IntraSubPartitionsSplitType isnot equal to ISP_NO_SPLIT; cu_sbt_flag is equal to 1 and Max(nTbW, nTbH)is less than or equal to 32 and sps_inter_mts_selection_flag is equal to1; and/or sps_intra_mts_selection is equal to 1 andCuPredMode[0][xTbY][yTbY] is equal to MODE_INTRA and lfnst_idx[x0][y0]is equal to 0 and intra_mip_flag[x0][y0] is equal to 0. Otherwise,implicitMtsEnabled is set equal to 0.

In another embodiment, the exemplary HLS syntaxes in Table 13 aredesigned for indicating the usage of MTS, where implicit MTS can beenabled for SBT without enabling explicit MTS.

TABLE 13 Syntaxes elments designed for indicating the usage of MTSseq_parameter_set_rbsp( ) { Descriptor ......  sps_intra_mts_selectionue(v)  sps_inter_mts_selection ue(v) ......As shown in Table 13, sps_intra_mts_selection can have a value of 0, 1,or 2. When sps_intra_mts_selection is equal to 0 or 1, tu_mts_idx is notpresent in the transform unit syntax for intra coding units. Whensps_intra_mts_selection is equal to 2, tu_mts_idx can be present in thetransform unit syntax for intra coding units. Moreover, whensps_intra_mts_selection is equal to 0, implicit MTS is not applied forintra prediction residuals. When sps_intra_mts_selection is equal to 1,implicit MTS is applied for intra prediction residuals.sps_inter_mts_selection can have a value of 0, 1, or 2. Whensps_inter_mts_selection is equal to 0 or 1, tu_mts_idx can be present inthe transform unit syntax for inter coding units. Whensps_inter_mts_selection is equal to 2, tu_mts_idx can be present in thetransform unit syntax for inter coding units. Further, whensps_inter_mts_selection is equal to 0, implicit MTS is not applied forinter prediction residuals. When sps_inter_mts_selection is equal to 1,implicit MTS is applied for inter prediction residuals. An exemplarysyntax designed for indicting the usage of MTS based on the syntaxelements in Table 13 is shown in Table 14 for example.

TABLE 14 Syntaxes designed for indicating the usage of MTS if( ( (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTER && sps_inter_mts_selection == 2 )  || ( CuPredMode[ chType ][ x0 ][ y0 ] == MODE_INTRA &&  sps_intra_mts_selection ==2) ) &&  (!transform_skip_flag[ x0 ][ y0 ] ) )  tu_mts_idx[ x0 ][ y0 ] ae(v)

An example of a modified transformation process for scaled transformcoefficients for some embodiments is described below. Inputs to thisprocess can include a luma location (xTbY, yTbY) specifying the top-leftsample of the current luma transform block relative to the top-left lumasample of the current picture; a variable nTbW specifying the width ofthe current transform block; a variable nTbH specifying the height ofthe current transform block; a variable cIdx specifying the colourcomponent of the current block; and/or an (nTbW)×(nTbH) array d[x][y] ofscaled transform coefficients with x=0 . . . nTbW−1, y=0 . . . nTbH−1.An output of this process is the (nTbW)×(nTbH) array r[x][y] of residualsamples with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

The variable implicitMtsEnabled can be derived as follows. If one of aplurality of conditions is true, implicitMtsEnabled is set equal to 1.The plurality of conditions can include IntraSubPartitionsSplitType isnot equal to ISP_NO_SPLIT; cu_sbt_flag is equal to 1 and Max(nTbW, nTbH)is less than or equal to 32 and sps-inter-mts-selection is not equal to0; and/or sps_intra_mts_selection is equal to 1 andCuPredMode[0][xTbY][yTbY] is equal to MODE_INTRA and lfnst_idx[x0][y0]is equal to 0 and intra_mip_flag[x0][y0] is equal to 0. Otherwise,implicitMtsEnabled is set equal to 0.

In the disclosure, a transform selection for ISP coded blocks can becontrolled by MTS related HLS to indicate whether implicit MTS or DCT-2is applied. An example of a modified transformation process for scaledtransform coefficients according to some embodiments is described below.Inputs to this process can include a luma location (xTbY, yTbY)specifying the top-left sample of the current luma transform blockrelative to the top-left luma sample of the current picture; a variablenTbW specifying the width of the current transform block; a variablenTbH specifying the height of the current transform block; a variablecIdx specifying the colour component of the current block; and/or an(nTbW)×(nTbH) array d[x][y] of scaled transform coefficients with x=0 .. . nTbW−1, y=0 . . . nTbH−1. An output of this process is the(nTbW)×(nTbH) array r[x][y] of residual samples with x=0 . . . nTbW−1,y=0 . . . nTbH−1.

The variable implicitMtsEnabled can be derived as follows. If one of aplurality of conditions is true, implicitMtsEnabled is set equal to 1.The plurality of conditions can include IntraSubPartitionsSplitType isnot equal to ISP_NO_SPLIT and sps_intra_mts_selection is not equal to 0;cu_sbt_flag is equal to 1 and Max(nTbW, nTbH) is less than or equal to32 and sps_inter_mts_selection is not equal to 0; and/orsps_intra_mts_selection is equal to 01 and CuPredMode[0][xTbY][yTbY] isequal to MODE_INTRA and lfnst_idx[x0][y0] is equal to 0 andintra_mip_flag[x0][y0] is equal to 0. Otherwise, implicitMtsEnabled isset equal to 0.

In some embodiments, the PDPC refers to a simplified PDPC mentionedabove or a variant thereof. In some embodiments, DST-4 may be used toreplace DST-7 for certain small block sizes or all block sizes.

In the disclosure, an “implicit transform” can indicate a transformscheme selecting a group of non-DCT2 transforms (such as DST-1, DCT-5,DST-7, DCT-8, DST-4, DCT-4) without any transform index signaling. Forexample, a group of non-DCT2 transforms can be selected using alreadycoded information that is available to both encoder and decoder,including but not limited to intra prediction mode (Planar mode, DCmode, Angular modes), block size, block width, block height, blockaspect ratio, block area size, intra coding mode (whether MRL, ISP, MIPis used), position of selected spatial Merge candidates (top Mergecandidate, left Merge candidate), and/or inter prediction mode(inter-PDPC mode, CIIP mode etc.).

In the disclosure, an “explicit transform” can indicate a transformscheme selecting one transform from a group of transform type candidates(such as DCT-2, DST-1, DCT-5, DST-7, DCT-8, DST-4, DCT-4) with an indexsignaled to indicate which transform type is selected.

In the disclosure, explicit MTS applied for an intra prediction residualcan be called explicit intra MTS, and MTS applied for an interprediction residual can be called explicit inter MTS.

FIG. 19 shows a flow chart outlining a process (1900) according to anembodiment of the disclosure. FIG. 20 shows a flow chart outlining aprocess (2000) according to an embodiment of the disclosure. FIG. 21shows a flow chart outlining a process (2100) according to an embodimentof the disclosure. In various embodiments, the process (1900), theprocess (2000), and the process (2100) can be executed by processingcircuitry, such as the processing circuitry in the terminal devices(110), (120), (130) and (140), the processing circuitry that performsfunctions of the video encoder (203), the processing circuitry thatperforms functions of the video decoder (210), the processing circuitrythat performs functions of the video decoder (310), the processingcircuitry that performs functions of the video encoder (403), and thelike. In some embodiments, the process (1900), the process (2000), andthe process (2100) can be implemented in software instructions, thuswhen the processing circuitry executes the software instructions, theprocessing circuitry performs the process (1900), the process (2000),and/or the process (2100) respectively.

As shown in FIG. 19, the process (1900) starts at (S1901) and proceedsto (S1910). At (S1910), prediction information of a current block in acurrent picture can be decoded from a coded video bitstream. Theprediction information is indicative of an inter prediction mode

At (S1920), whether a filtering process is applied on the current blockcan be determined. The filtering process can adjust inter predictionsamples of the current block based on neighboring reconstructed samplesof the current block. In some embodiments, the filtering process can beoperated based on a position dependent prediction combination (PDPC)mode or a combined inter and intra prediction (CIIP) mode.

At (S1930), a primary transform can be performed for a transform blockaccording to a pre-defined primary transform type based on the filteringprocess being determined to be applied on the current block, where thetransform block is partitioned from the current block.

In some embodiments, the primary transform type can be a type-7 discretesine transform (DST-7) mode for a horizontal transform that is appliedto the transform block responsive to a width of the current block beingsmaller than or equal to a threshold value. The primary transform typecan be the DST-7 mode for a vertical transform that is applied to thetransform block responsive to a height of the current block beingsmaller than or equal to the threshold value. The threshold value caninclude one of 4 pixels, 8 pixels, 16 pixels, or 32 pixels.

In some embodiments, the primary transform type can be a type-2 discretecosine transform (DCT-2) mode for a horizontal transform that is appliedto the transform block responsive to a width of the current block beingbigger than to a threshold value. The primary transform type can be theDCT-2 mode for a vertical transform and can be applied to the transformblock responsive to a height of the current block being larger than thethreshold value. The threshold value can include one of 4 pixels, 8pixels, 16 pixels, or 32 pixels.

As shown in FIG. 20, the process (2000) starts at (S2001) and proceedsto (S2010). At (S2010), prediction information of a current block can beacquired from a coded video bitstream.

At (S2020), whether the prediction information indicates (i) an interprediction merge mode, and (ii) a combined inter and intra prediction(CIIP) mode can be determined.

At (S2030), an intra prediction mode can be determined from an intraprediction mode candidate list responsive to the prediction informationindicating the inter prediction merge mode and the CIIP mode.

At (S2040), intra prediction information can be determined according tothe intra prediction mode and inter prediction information according tothe inter prediction merge mode.

At (S2050), a weighting factor can be determined responsive toneighboring blocks of the current block being coded according to theCIIP mode or an inter position dependent prediction combination (PDPC)mode.

In some embodiments, the weighted inter prediction information is basedon the inter prediction information and a constant value minus theweighting factor, where the constant value includes one of 2, 4, 8, or16.

In some embodiments, the weighting factor can be 3 responsive to bothtop-right/top and bottom-left/left neighboring blocks of the currentblock being coded using the CIIP mode. In some embodiments, theweighting factor can be 2 responsive to one of the top-right/top and thebottom-left/left neighboring blocks of the current block being codedusing the CIIP mode. In some embodiments, the weighting factor can be 1responsive to the top-right/top and the bottom-left/left neighboringblocks of the current block being coded using the CIIP mode.

In some embodiments, the weighting factor can be 3 responsive to bothtop-right/top and bottom-left/left neighboring blocks of the currentblock being coded using the PDPC mode. The weighting factor can be 2responsive to one of the top-right/top and the bottom-left/leftneighboring blocks of the current block being coded using the PDPC mode.The weighting factor can be 1 responsive to none of the top-right/topand the bottom-left/left neighboring blocks of the current block beingcoded using the PDPC mode.

At (S2060), CIIP prediction information can be determined based on a sumof weighted intra prediction information and weighted inter predictioninformation, where the weighted intra prediction information is based onthe intra prediction information and the weighting factor, and theweighted inter prediction information is based on the inter predictioninformation and the weighting factor.

The process (2000) then proceeds to (S2070) where a sample of thecurrent block can be reconstructed according to the CIIP predictioninformation.

FIG. 21 illustrates the process (2100) that starts at (S2101) andproceeds to (S2110). At (S2110), transform block signaling informationcan be acquired from a coded video bitstream. The transform blocksignaling information can include first information associated with aninter prediction transform and second information associated with anintra prediction transform.

At (S2120), a first value of the first information and a second value ofthe second information can be determined.

At (S2130), a first transform block coded in an inter prediction modecan be transformed according to the first value and a first pre-definedtransform type in an implicit multiple transform selection (MTS) mode.

At (S2140), a second transform block coded in an intra prediction modecan be transformed according to a second value and a second pre-definedtransform type in the implicit MTS mode.

In some embodiments, the first value of the first information can beequal to 1 and the second value of the second information can be equalto 1.

In some embodiments, the first value of the first information can begreater than 0, and the second value of the second information can beequal to 1.

In some embodiments, the second transform block coded in the intraprediction mode can be transformed according to the second value, thesecond pre-defined transform type in the implicit MTS mode, and a codingunit that includes the second transform block being intrasub-partitioning (ISP) coded. The second value is larger than 0.

The proposed methods may be used separately or combined in any order.Further, each of the methods (or embodiments), encoder, and decoder maybe implemented by processing circuitry (e.g., one or more processors orone or more integrated circuits). In one example, the one or moreprocessors execute a program that is stored in a non-transitorycomputer-readable medium. For example, the techniques described above,can be implemented as computer software using computer-readableinstructions and physically stored in one or more computer-readablemedia. FIG. 22 shows an exemplary computer system (2200) suitable forimplementing certain embodiments of the disclosed subject matter.

The computer software can be coded using any suitable machine code orcomputer language, that may be subject to assembly, compilation,linking, or like mechanisms to create code comprising instructions thatcan be executed directly, or through interpretation, micro-codeexecution, and the like, by one or more computer central processingunits (CPUs), Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers orcomponents thereof, including, for example, personal computers, tabletcomputers, servers, smartphones, gaming devices, internet of thingsdevices, and the like.

The components shown in FIG. 22 for computer system (2200) are exemplaryin nature and are not intended to suggest any limitation as to the scopeof use or functionality of the computer software implementingembodiments of the present disclosure. Neither should the configurationof components be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theexemplary embodiment of a computer system (2200).

Computer system (2200) may include certain human interface inputdevices. Such a human interface input device may be responsive to inputby one or more human users through, for example, tactile input (such as:keystrokes, swipes, data glove movements), audio input (such as: voice,clapping), visual input (such as: gestures), olfactory input (notdepicted). The human interface devices can also be used to capturecertain media not necessarily directly related to conscious input by ahuman, such as audio (such as: speech, music, ambient sound), images(such as: scanned images, photographic images obtain from a still imagecamera), video (such as two-dimensional video, three-dimensional videoincluding stereoscopic video).

Input human interface devices may include one or more of (only one ofeach depicted): keyboard (2201), mouse (2202), trackpad (2203), touchscreen (2210), data-glove (not shown), joystick (2205), microphone(2206), scanner (2207), camera (2208).

Computer system (2200) may also include certain human interface outputdevices. Such human interface output devices may be stimulating thesenses of one or more human users through, for example, tactile output,sound, light, and smell/taste. Such human interface output devices mayinclude tactile output devices (for example tactile feedback by thetouch-screen (2210), data-glove (not shown), or joystick (2205), butthere can also be tactile feedback devices that do not serve as inputdevices), audio output devices (such as: speakers (2209), headphones(not depicted)), visual output devices (such as screens (2210) toinclude CRT screens, LCD screens, plasma screens, OLED screens, eachwith or without touch-screen input capability, each with or withouttactile feedback capability—some of which may be capable to output twodimensional visual output or more than three dimensional output throughmeans such as stereographic output; virtual-reality glasses (notdepicted), holographic displays and smoke tanks (not depicted)), andprinters (not depicted).

Computer system (2200) can also include human accessible storage devicesand their associated media such as optical media including CD/DVD ROM/RW(2020) with CD/DVD or the like media (2221), thumb-drive (2222),removable hard drive or solid state drive (2223), legacy magnetic mediasuch as tape and floppy disc (not depicted), specialized ROM/ASIC/PLDbased devices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computerreadable media” as used in connection with the presently disclosedsubject matter does not encompass transmission media, carrier waves, orother transitory signals.

Computer system (2200) can also include an interface to one or morecommunication networks. Networks can for example be wireless, wireline,optical. Networks can further be local, wide-area, metropolitan,vehicular and industrial, real-time, delay-tolerant, and so on. Examplesof networks include local area networks such as Ethernet, wireless LANs,cellular networks to include GSM, 3G, 4G, 5G, LTE and the like, TVwireline or wireless wide area digital networks to include cable TV,satellite TV, and terrestrial broadcast TV, vehicular and industrial toinclude CANBus, and so forth. Certain networks commonly require externalnetwork interface adapters that attached to certain general purpose dataports or peripheral buses (2249) (such as, for example USB ports of thecomputer system (2200)); others are commonly integrated into the core ofthe computer system (2200) by attachment to a system bus as describedbelow (for example Ethernet interface into a PC computer system orcellular network interface into a smartphone computer system). Using anyof these networks, computer system (2200) can communicate with otherentities. Such communication can be uni-directional, receive only (forexample, broadcast TV), uni-directional send-only (for example CANbus tocertain CANbus devices), or bi-directional, for example to othercomputer systems using local or wide area digital networks. Certainprotocols and protocol stacks can be used on each of those networks andnetwork interfaces as described above.

Aforementioned human interface devices, human-accessible storagedevices, and network interfaces can be attached to a core (2240) of thecomputer system (2200).

The core (2240) can include one or more Central Processing Units (CPU)(2241), Graphics Processing Units (GPU) (2242), specialized programmableprocessing units in the form of Field Programmable Gate Areas (FPGA)(2243), hardware accelerators for certain tasks (2244), and so forth.These devices, along with Read-only memory (ROM) (2245), Random-accessmemory (2246), internal mass storage such as internal non-useraccessible hard drives, SSDs, and the like (2247), may be connectedthrough a system bus (2248). In some computer systems, the system bus(2248) can be accessible in the form of one or more physical plugs toenable extensions by additional CPUs, GPU, and the like. The peripheraldevices can be attached either directly to the core's system bus (2248),or through a peripheral bus (2249). Architectures for a peripheral businclude PCI, USB, and the like.

CPUs (2241), GPUs (2242), FPGAs (2243), and accelerators (2244) canexecute certain instructions that, in combination, can make up theaforementioned computer code. That computer code can be stored in ROM(2245) or RAM (2246). Transitional data can be also be stored in RAM(2246), whereas permanent data can be stored for example, in theinternal mass storage (2247). Fast storage and retrieve to any of thememory devices can be enabled through the use of cache memory, that canbe closely associated with one or more CPU (2241), GPU (2242), massstorage (2247), ROM (2245), RAM (2246), and the like.

The computer readable media can have computer code thereon forperforming various computer-implemented operations. The media andcomputer code can be those specially designed and constructed for thepurposes of the present disclosure, or they can be of the kind wellknown and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system havingarchitecture (2200), and specifically the core (2240) can providefunctionality as a result of processor(s) (including CPUs, GPUs, FPGA,accelerators, and the like) executing software embodied in one or moretangible, computer-readable media. Such computer-readable media can bemedia associated with user-accessible mass storage as introduced above,as well as certain storage of the core (2240) that are of non-transitorynature, such as core-internal mass storage (2247) or ROM (2245). Thesoftware implementing various embodiments of the present disclosure canbe stored in such devices and executed by core (2240). Acomputer-readable medium can include one or more memory devices orchips, according to particular needs. The software can cause the core(2240) and specifically the processors therein (including CPU, GPU,FPGA, and the like) to execute particular processes or particular partsof particular processes described herein, including defining datastructures stored in RAM (2246) and modifying such data structuresaccording to the processes defined by the software. In addition or as analternative, the computer system can provide functionality as a resultof logic hardwired or otherwise embodied in a circuit (for example:accelerator (2244)), which can operate in place of or together withsoftware to execute particular processes or particular parts ofparticular processes described herein. Reference to software canencompass logic, and vice versa, where appropriate. Reference to acomputer-readable media can encompass a circuit (such as an integratedcircuit (IC)) storing software for execution, a circuit embodying logicfor execution, or both, where appropriate. The present disclosureencompasses any suitable combination of hardware and software.

APPENDIX A: ACRONYMS

JEM: joint exploration modelVVC: versatile video codingBMS: benchmark set

MV: Motion Vector HEVC: High Efficiency Video Coding SEI: SupplementaryEnhancement Information VUI: Video Usability Information GOPs: Groups ofPictures TUs: Transform Units, PUs: Prediction Units CTUs: Coding TreeUnits CTBs: Coding Tree Blocks PBs: Prediction Blocks HRD: HypotheticalReference Decoder SNR: Signal Noise Ratio CPUs: Central Processing UnitsGPUs: Graphics Processing Units CRT: Cathode Ray Tube LCD:Liquid-Crystal Display OLED: Organic Light-Emitting Diode CD: CompactDisc DVD: Digital Video Disc ROM: Read-Only Memory RAM: Random AccessMemory ASIC: Application-Specific Integrated Circuit PLD: ProgrammableLogic Device LAN: Local Area Network

GSM: Global System for Mobile communications

LTE: Long-Term Evolution CANBus: Controller Area Network Bus USB:Universal Serial Bus PCI: Peripheral Component Interconnect FPGA: FieldProgrammable Gate Areas

SSD: solid-state drive

IC: Integrated Circuit CU: Coding Unit

While this disclosure has described several exemplary embodiments, thereare alterations, permutations, and various substitute equivalents, whichfall within the scope of the disclosure. It will thus be appreciatedthat those skilled in the art will be able to devise numerous systemsand methods which, although not explicitly shown or described herein,embody the principles of the disclosure and are thus within the spiritand scope thereof.

What is claimed is:
 1. A method of video decoding for a decoder, themethod comprising: decoding prediction information of a current block ina current picture from a coded video bitstream, the predictioninformation being indicative of an inter prediction mode; determiningwhether a filtering process is applied on the current block, wherein thefiltering process adjusts inter prediction samples of the current blockbased on neighboring reconstructed samples of the current block; andperforming a primary transform for a transform block according to apre-defined primary transform type based on the filtering process beingdetermined to be applied on the current block, the transform block beingpartitioned from the current block.
 2. The method of claim 1, whereinthe filtering process is operated based on a position dependentprediction combination (PDPC) mode or a combined inter and intraprediction (CIIP) mode.
 3. The method of claim 1, wherein: thepre-defined primary transform type is a type-7 discrete sine transform(DST-7) mode for a horizontal transform that is applied to the transformblock responsive to a width of the current block being smaller than orequal to a threshold value, the pre-defined primary transform type isthe DST-7 mode for a vertical transform that is applied to the transformblock responsive to a height of the current block being smaller than orequal to the threshold value, and the threshold value includes one of 4pixels, 8 pixels, 16 pixels, or 32 pixels.
 4. The method of claim 1,wherein the pre-defined primary transform type is a type-2 discretecosine transform (DCT-2) mode for a horizontal transform that is appliedto the transform block responsive to a width of the current block beingbigger than to a threshold value, the pre-defined primary transform typeis the DCT-2 mode for a vertical transform is applied to the transformblock responsive to a height of the current block being larger than thethreshold value, and the threshold value includes one of 4 pixels, 8pixels, 16 pixels, or 32 pixels.
 5. The method of claim 1, wherein thepre-defined primary transform type is a transform skip mode (TSM), aDCT-2 mode, or a DST-7 mode.
 6. The method of claim 1, wherein thefiltering process is a boundary filtering process in which at least oneof rows adjacent to a boundary of the current block or at least one ofcolumns adjacent to the boundary of the current block are adjusted basedon the filtering process.
 7. The method of claim 1, wherein thefiltering process applies position-dependent weightings between theinter prediction samples of the current block and the neighboringreconstructed samples of the current block.
 8. The method of claim 1,wherein the pre-defined primary transform type is implicit for a lumacomponent of the current block, and a DCT-2 mode or a transform skipmode for a chroma component of the current block.
 9. The method of claim2, wherein: the pre-defined primary transform type is a type-7 discretesine transform (DST-7) mode for a horizontal transform that is appliedto the transform block responsive to (i) the filtering process beingoperated in the CIIP mode with a ratio of W_(intra)/W_(inter) beinglarger than a first threshold, and (ii) a width of the current blockbeing smaller than or equal to a second threshold value, the primarytransform type is the DST-7 mode for a vertical transform that isapplied to the transform block responsive to (i) the filtering processbeing operated in the CIIP mode with the ratio of W_(intra)/W_(inter)being larger than the first threshold, and (ii) a height of the currentblock being smaller than or equal to the second threshold value, thefirst threshold value includes one of 2, 2.5, 3, or 7, the secondthreshold value includes one of 4 pixels, 8 pixels, 16 pixels, or 32pixels, and W_(intra) is an intra weighting factor applied on an intraprediction information of the current block, and W_(inter) is an interweighting factor applied on an inter prediction information of thecurrent block,
 10. The method of claim 2, wherein: the pre-definedprimary transform type is a type-7 discrete sine transform (DST-7) modefor a horizontal transform that is applied to the transform blockresponsive to (i) the filtering process being operated based on the CIIPmode, (ii) both above and left neighboring blocks of the current blockbeing intra coded, and (iii) a width of the current block being smallerthan or equal to a threshold value; and the pre-defined primarytransform type is the DST-7 mode for a vertical transform that isapplied to the transform block responsive to (i) the filtering processbeing operated in the CIIP mode, (ii) both the above and the leftneighboring blocks of the current block being intra coded, and (ii) aheight of the current block being smaller than or equal to the thresholdvalue, the threshold value including one of 4 pixels, 8 pixels, 16pixels, or 32 pixels.
 11. The method of claim 1, wherein: thepre-defined primary transform type is a type-7 discrete sine transform(DST-7) mode for a horizontal transform that is applied to the transformblock responsive to (i) the filtering process being operated based onthe CIIP mode, (ii) a subset of above and left neighboring blocks of thecurrent block being intra coded, (iii) a width of the current blockbeing smaller than or equal to a threshold value; and the pre-definedprimary transform type is the DST-7 mode for a vertical transform thatis applied to the transform block responsive to (i) the filteringprocess being operated based on the CIIP mode, (ii) the subset of theabove and the left neighboring blocks of the current block being intracoded, and (iii) a height of the current block being smaller than orequal to the threshold value, the threshold value including one of 4pixels, 8 pixels, 16 pixels, or 32 pixels.
 12. The method of claim 2,further comprising: determining a context model from a set of contextmodels based on the prediction information, the prediction informationindicating the filtering process based on the PDPC mode being applied tothe current block; and decoding primary transform type information basedon the determined context model, the primary transform type informationindicating whether the pre-defined primary transform type includes oneof a transform skip mode (TSM), a DCT-2 mode, a DST-7 mode, or a DCT-8mode.
 13. A method of video decoding for a decoder, the methodcomprising: acquiring prediction information of a current block from acoded video bitstream, determining whether the prediction informationindicates (i) an inter prediction merge mode, and (ii) a combined interand intra prediction (CIIP) mode; determining an intra prediction modefrom an intra prediction mode candidate list responsive to theprediction information indicating the inter prediction merge mode andthe CIIP mode; determining intra prediction information according to theintra prediction mode and inter prediction information according to theinter prediction merge mode; determining a weighting factor responsiveto neighboring blocks of the current block being coded according to theCIIP mode or an inter position dependent prediction combination (PDPC)mode; determining CIIP prediction information based on a sum of weightedintra prediction information and weighted inter prediction information,the weighted intra prediction information being based on the intraprediction information and the weighting factor, the weighted interprediction information being based on the inter prediction informationand the weighting factor; and reconstructing a sample of the currentblock according to the CIIP prediction information.
 14. The method ofclaim 13, wherein the weighted inter prediction information is based onthe inter prediction information and a constant value minus theweighting factor, the constant value including one of 2, 4, 8, or 16.15. The method of claim 14, wherein: the weighting factor is 3responsive to both top-right/top and bottom-left/left neighboring blocksof the current block being coded using the CIIP mode, the weightingfactor is 2 responsive to one of the top-right/top and thebottom-left/left neighboring blocks of the current block being codedusing the CIIP mode, and the weighting factor is 1 responsive to thetop-right/top and the bottom-left/left neighboring blocks of the currentblock being coded using the CIIP mode.
 16. The method of claim 15,wherein: the weighting factor is 3 responsive to both top-right/top andbottom-left/left neighboring blocks of the current block being codedusing the PDPC mode; the weighting factor is 2 responsive to one of thetop-right/top and the bottom-left/left neighboring blocks of the currentblock being coded using the PDPC mode; and the weighting factor is 1responsive to none of the top-right/top and the bottom-left/leftneighboring blocks of the current block being coded using the PDPC mode;17. A method of video decoding for a decoder, the method comprising:acquiring transform block signaling information from a coded videobitstream, the transform block signaling information including firstinformation associated with an inter prediction transform and secondinformation associated with an intra prediction transform; determining afirst value of the first information and a second value of the secondinformation; transforming a first transform block coded in an interprediction mode according to the first value and a first pre-definedtransform type in an implicit multiple transform selection (MTS) mode;and transforming a second transform block coded in an intra predictionmode according to a second value and a second pre-defined transform typein the implicit MTS mode.
 18. The method of claim 17, wherein the firstvalue of the first information is equal to 1 and the second value of thesecond information is equal to
 1. 19. The method of claim 17, whereinthe first value of the first information is greater than 0, and thesecond value of the second information is equal to
 1. 20. The method ofclaim 17, wherein the transforming the second transform block comprises:transforming the second transform block coded in the intra predictionmode according to the second value, the second pre-defined transformtype in the implicit MTS mode, and a coding unit that includes thesecond transform block being intra sub-partitioning (ISP) coded, thesecond value being larger than 0.